delivered the opinion of the court:
In this interlocutory appeal, defendant, Murray Blue, asks the court to decide whether principles of collateral estoppel embodied in the double jeopardy protections of our state and federal constitutions (U.S. Const., amend. V; Ill. Const. 1970, art. I, § 10) bar the State from seeking the death penalty should defendant be convicted for the first degree murder of Louis Moret upon retrial. We find that, under the circumstances presented, double jeopardy principles do not preclude the State from attempting to secure a death sentence.
*545BACKGROUND
On March 8, 1995, defendant was arrested and charged with multiple crimes, including the first degree murder of Chicago police officer Daniel Doffyn, in relation to two separate shooting incidents which occurred that day. See People v. Blue, 189 Ill. 2d 99 (2000). That same day, defendant was also charged with the February 26, 1995, murder of Louis Moret, pursuant to a warrant issued March 4, 1995. See Blue, 189 Ill. 2d at 114.
The State opted to try the Doffyn murder and related crimes first. After a jury trial in the circuit court of Cook County, defendant was found guilty of the first degree murder of Officer Doffyn, as well as three counts of attempted first degree murder, two counts of aggravated battery with a firearm, and two counts of possession of a controlled substance with the intent to deliver. Blue, 189 Ill. 2d at 103. With respect to the first degree murder conviction, the trial court imposed the death penalty after the jury found defendant eligible based on the statutory aggravating factor found in section 9 — 1(b)(1) of the Criminal Code of 1961, that the “murdered individual was a peace officer *** killed in the course of performing his official duties, *** and the defendant knew or should have known that the murdered individual was a peace officer” (720 ILCS 5/9 — 1(b)(1) (West 1998)), and that there were no mitigating factors sufficient to preclude imposition of the death sentence. See Blue, 189 Ill. 2d at 103. Defendant then brought a direct appeal to this court (134 IU. 2d R. 302(b)).
While the appeal of defendant’s conviction and sentence for Officer Doffyn’s murder was pending, defendant was tried for Moret’s murder and found guilty. Again, the State sought the death penalty, this time arguing that defendant was eligible under the multiple-murder aggravating factor because defendant had been convicted of murdering two individuals. 720 ILCS 5/9— 1(b)(3) (West 1998). Defendant was sentenced to death *546after the jury found defendant eligible under section 9 — 1(b)(3) and, further, that there were no mitigating circumstances sufficient to preclude imposition of the death sentence. See People v. Blue, 205 Ill. 2d 1, 3 (2001). Defendant appealed this conviction and sentence directly to this court.
On January 27, 2000, this court issued an opinion with regard to defendant’s first appeal. We held that defendant was denied a fair trial because of cumulative errors which occurred during defendant’s trial for the murder of Officer Doffyn. As a result, defendant’s convictions were reversed and the cause remanded for a new trial. People v. Blue, 189 Ill. 2d 99 (2000). Shortly thereafter, defendant was retried and again found guilty of Officer Doffyn’s murder. At defendant’s capital sentencing hearing the State argued that defendant was eligible for the death penalty pursuant to section 9 — 1(b)(1), because the murdered individual was a peace officer. In addition, the State argued that defendant was also eligible for the death penalty pursuant to section 9 — 1(b)(3), because defendant now stood convicted for the first degree murder of a second individual, Louis Moret. 720 ILCS 5/9 — 1(b)(1), (b)(3) (West 1998). The jury found defendant eligible for the death penalty under both statutory factors. Nevertheless, the jury declined to sentence defendant to death and the trial court imposed a sentence of natural life in prison.
After defendant was retried and sentenced for the Doffyn murder, the direct appeal of his conviction for the murder of Louis Moret came before this court. On September 27, 2001, this court reversed that conviction and remanded for a new trial, finding that the trial court had improperly limited defendant’s cross-examination of certain key State witnesses. People v. Blue, 205 Ill. 2d 1 (2001). Prior to retrial, defendant filed a motion in the circuit court seeking to bar the State from initiating *547death penalty procedures should he again be convicted of Moret’s murder. Defendant posited that implicit in the section 9 — 1(b)(3) statutory aggravating factor is the notion that a defendant convicted of first degree murder for the first time is not eligible for the death penalty and that it is only after defendant’s second conviction for first degree murder that he becomes death eligible. Extrapolating from this concept, defendant theorized that when a defendant is tried separately for the commission of two unrelated murders, as is the case here, one of the murder convictions, logically, must be the first conviction, while the other murder conviction must be the second conviction. Expanding on this theory, defendant contended that if a person is convicted of committing two separate, unrelated murders and the multiple-murder aggravating factor (720 ILCS 5/9 — 1(b)(3) (West 1998)) is the sole basis for finding that person eligible for the death penalty, the State can have only one opportunity to seek the death penalty with respect to these two murders. He further contended that, once the State tries the defendant for one of the two murders, obtains a conviction, and uses that conviction as the aggravating factor to seek the death penalty at the trial for the other murder, the earlier conviction is determined to be the “first conviction.” The State is then bound by that determination and, with respect to those two murders, principles of collateral estoppel prevent the State from later “reversing the order” of these convictions.
Applying this theory to his current situation, defendant contended that when the jury found him eligible for the death penalty pursuant to section 9 — 1(b)(3) following his retrial for the murder of Officer Doffyn, the jury made a legally binding determination that the Moret murder was defendant’s “first conviction” and, thus by definition, the non-death-eligible conviction. Accordingly, defendant concluded that the State should be barred by *548principles of collateral estoppel embodied in the double jeopardy protections of our state and federal constitutions from attempting to establish the Doffyn murder as defendant’s first conviction to prove defendant eligible for the death sentence under section 9 — 1(b)(3) for the murder of Moret at his retrial.
Defendant also argued that when the jury declined to impose the death penalty after defendant’s retrial for the murder of Officer Doffyn, that verdict was “a final judgement that determined whether the defendant is to be given death on the convictions of killing Daniel Doffyn and Louis Moret.” Accordingly, defendant argued that “the verdict of no death based upon the [two convictions] is an acquittal on the death issue based upon [the section 9 — 1(b)(3)] aggravating factor and a new death hearing is barred by double jeopardy.”
The trial court rejected defendant’s arguments and denied defendant’s motion to bar the State from initiating death penalty proceedings. Defendant then brought an interlocutory appeal pursuant to Supreme Court Rule 604(f) (188 Ill. 2d R. 604(f)). This court assumed jurisdiction over the matter pursuant to Supreme Court Rule 302(b) (134 Ill. 2d R. 302(b)).
ANALYSIS
The double jeopardy clause contained within the fifth amendment to the United States Constitution provides: “[N]or shall any person be subject for the same offence to be twice put in jeopardy of life or limb.” U.S. Const., amend. V There are three separate protections embraced by this double jeopardy clause: (1) protection against retrial for the same offense after an acquittal, (2) protection against retrial for the same offense after a conviction, and (3) protection against multiple punishment for the same offense. North Carolina v. Pearce, 395 U.S. 711, 717, 23 L. Ed. 2d 656, 664-65, 89 S. Ct. 2072, 2076 (1969); People v. Stefan, 146 Ill. 2d 324, 333 (1992). These protec*549tions are also guaranteed by the Illinois Constitution of 1970, which provides that “[n]o person shall be *** twice put in jeopardy for the same offense.” Ill. Const. 1970, art. I, § 10; People v. Levin, 157 Ill. 2d 138 (1993).
As a general rule, the protections afforded by the double jeopardy clause are limited to the “same offense.” Witte v. United States, 515 U.S. 389, 132 L. Ed. 2d 351, 115 S. Ct. 2199 (1995). However, because collateral estoppel principles are embodied in the constitutional guarantee against double jeopardy (Ashe v. Swenson, 397 U.S. 436, 25 L. Ed. 2d 469, 90 S. Ct. 1189 (1970)), an issue of ultimate fact, if determined by a valid and final judgment, may not be relitigated in a future proceeding. This does not mean, however, that “the double jeopardy clause *** prevent[s] a state from selecting a penalty independently for each crime a person commits.” Kokoraleis v. Gilmore, 131 F.3d 692, 695 (7th Cir. 1997). Nor does it violate double jeopardy principles for a defendant to be convicted and sentenced for a crime even though the conduct underlying that offense has been considered in determining the defendant’s sentence for a previous conviction. Witte v. United States, 515 U.S. at 398, 132 L. Ed. 2d at 363, 115 S. Ct. at 2205; Williams v. Oklahoma, 358 U.S. 576, 3 L. Ed. 2d 516, 79 S. Ct. 421 (1959).
Applying the above principles, the Seventh Circuit Court of Appeals ruled that collateral estoppel does not apply to prohibit a State from seeking capital punishment a second time for the same series of murders that was before a prior jury. Kokoraleis, 131 F.3d at 695. In Kokoraleis, the defendant was a serial killer who had confessed to murdering as many as 18 women. Defendant was tried and convicted for the murder of Rose Beck Davis, but the jury decided not to impose the death penalty. Thereafter, defendant was convicted for the murder of Lori Borowski and sentenced to death. He appealed his death sentence, claiming that capital punish*550ment for the Borowski murder was precluded by the fact that the other jury had decided not to impose the death penalty. The court held:
“Kokoraleis tells us that the question decided by the jury in the Cook County prosecution was ‘whether he should be put to death for torturing and being a serial killer of sixteen to eighteen women.’ Phrasing the question in this way makes it possible to say that the two juries decided the same issue. But this is not the question either jury decided. The Cook County jury selected the punishment for the murder of Rose Beck Davis; the DuPage County jury chose the punishment for the murder of Lori Borowski. Each jury was entitled to consider facts about Kokoraleis’ background, including his other criminal acts (which by the time of the prosecution for the Borowski murder included a prior murder conviction), but this does not mean that the punishment in a given case is for these other crimes; it is for the crime of which the defendant now stands convicted.” Kokoraleis, 131 E3d at 695.
In the case at bar, defendant raised the same argument made by the defendant in Kokoraleis and the trial court rejected it. Defendant has since abandoned this argument in his appeal before this court.1 Consequently, the only argument which defendant has presented for our consideration is whether the State is precluded from seeking the death penalty at defendant’s retrial for Moret’s murder because the jury at defendant’s resentencing for Doffyn’s murder “ruled” that the Moret murder was defendant’s “first conviction.”
Before addressing this argument, we examine the statutory provision at issue here. Section 9 — 1(b)(3) of the Illinois death penalty statute provides:
*551“(b) Aggravating Factors. A defendant who at the time of the commission of the offense has attained the age of 18 or more and who has been found guilty of first degree murder may be sentenced to death if:
* * ❖
(3) the defendant has been convicted of murdering two or more individuals under subsection (a) of this Section or under any law of the United States or of any state which is substantially similar to subsection (a) of this Section regardless of whether the deaths occurred as the result of the same act or of several related or unrelated acts so long as the deaths were the result of either an intent to kill more than one person or of separate acts which the defendant knew would cause death or create a strong probability of death or great bodily harm to the murdered individual or another[.]” 720 ILCS 5/9 — 1(b)(3) (West 1998).
In People v. Albanese, 104 Ill. 2d 504, 533-34 (1984), we interpreted the phrase “has been convicted of’ as used in section 9 — 1(b)(3) and concluded that “[t]he statute speaks in terms of prior convictions, not prior offenses.” We held that when a defendant, like the defendant in the case at bar, commits two murders on two separate dates and he is tried first for the murder which occurred on a later date, that conviction may be used as an aggravating factor at the trial of the other murder, which occurred earlier in time. We concluded that it was the sequence of convictions, not the sequence of conduct, which determines whether or not the multiple-murder aggravating-factor provision applies in a given case. People v. Johnson, 182 Ill. 2d 96, 109 (1998); People v. Guest, 115 Ill. 2d 72, 105 (1986).
Our own examination of the statutory language convinces us that the statute clearly provides that a defendant will be eligible for the death penalty if it is shown that he “has been convicted of murdering two or more individuals *** whether the deaths occurred as the result of the same act or of several related or unrelated *552acts.” Nothing in the statutory language suggests that a capital sentencing jury is required to make a factual determination as to the order of these convictions. The jury simply must find whether, at the time of sentencing, the defendant stands convicted of two or more first degree murders.
It follows, then, that in the case at bar, the Doffyn sentencing jury made no factual determination, legally binding or otherwise, that the Moret murder was defendant’s “first conviction.” The jury merely found that, at the time of defendant’s second sentencing hearing for Doffyn’s murder, defendant had another conviction for first degree murder. Thus, the jury’s finding that the section 9 — 1(b)(3) aggravating factor was proved at defendant’s retrial for the murder of Officer Doffyn has no collateral impact on the State’s ability to seek the death penalty in the case at bar.
Furthermore, even if defendant was correct in his premise that the Doffyn jury implicitly ruled that defendant’s prior conviction for the murder of Moret was defendant’s “first conviction” for purposes of death eligibility under section 9 — 1(b)(3), that prior conviction no longer exists. The “slate was wiped clean” when this court reversed on appeal defendant’s conviction for Móret’s murder. See Poland v. Arizona, 476 U.S. 147, 152, 90 L. Ed. 2d 123, 130, 106 S. Ct. 1749, 1753 (1986) (the usual rule is that, when a defendant obtains reversal of his conviction on appeal, the original conviction has been nullified and the slate wiped clean); Bullington v. Missouri, 451 U.S. 430, 443, 68 L. Ed. 2d 270, 281-82, 101 S. Ct. 1852, 1860 (1981).
Although we reject defendant’s contention that a murder conviction which occurs, chronologically, before another conviction remains the “first conviction” despite subsequent reversal, we recognize that there is an interdependent relationship which exists between a *553defendant’s murder convictions when they are used to establish death eligibility pursuant to section 9 — 1(b)(3). In Johnson v. Mississippi, 486 U.S. 578, 100 L. Ed. 2d 575, 108 S. Ct. 1981 (1988), the United States Supreme Court reversed a defendant’s death sentence when a prior murder conviction, which served as an aggravating factor, was reversed on appeal. The Court held:
“Since that conviction has been reversed, unless and until petitioner should be retried, he must be presumed innocent of that charge. Indeed, even without such a presumption, the reversal of the conviction deprives the prosecutor’s sole piece of documentary evidence of any relevance to Mississippi’s sentencing decision.” Johnson, 486 U.S. at 585, 100 L. Ed. 2d at 584, 108 S. Ct. at 1986.
Similarly, the Florida Supreme Court in Oats v. State, 446 So. 2d 90 (Fla. 1984), when considering a situation where an aggravating circumstance of a prior conviction, valid at the time of sentencing, is subsequently reversed and vacated by an appellate court, stated:
“We now hold that in such a situation the vacated conviction cannot be used as an aggravating factor. Therefore, the trial court was in error in finding this aggravating circumstance present.” Oats, 446 So. 2d at 95.
What these cases mean to the defendant here is that, had the multiple-murder aggravating factor been the only basis for finding defendant death eligible in the Doffyn case and had the jury imposed the death penalty in that case, the reversal of the Moret murder conviction might have supplied defendant with grounds for obtaining resentencing in the Doffyn case.
In the case at bar, however, defendant will receive a new trial on the question of his guilt for the murder of Louis Moret. If he is found guilty, the question before the capital sentencing jury will be whether, at the time of sentencing, defendant has been convicted of committing two or more murders. If the jury finds the “has been convicted of murdering two or more individuals” factor to exist, defendant shall be eligible for a death sentence.
*554The State is not precluded by collateral estoppel principles from using defendant’s conviction for Officer Doffyn’s murder to establish defendant’s eligibility for the death sentence.
Our conclusion in this case is supported by the Florida Supreme Court decision in Oats. In that case, the court noted that the defendant had subsequently received a new trial on the offenses underlying his earlier convictions which had been vacated. The new trial had resulted in convictions, which were upheld on review. The court held:
“Although the use of this aggravating factor was in error at the time it was found, and we therefore disallow it, were we to remand for a new penalty phase trial the jury could properly consider evidence of the later, valid conviction.” Oats, 446 So. 2d at 95.
As a final matter, defendant’s counsel, at oral argument, raised an arbitrariness argument. He contended that it would be arbitrary to allow the State to reverse or interchange the order of convictions to create death eligibility under section 9 — 1(b)(3) for both murders. Under Supreme Court Rule 341(e)(7), this argument is untimely and thus has been waived.
CONCLUSION
We find no merit to defendant’s claim that principles of collateral estoppel embodied in the double jeopardy protections of our state and federal constitutions (U.S. Const., amend. V; Ill. Const. 1970, art. I, § 10) bar the State from seeking the death penalty should defendant be convicted for the first degree murder of Louis Moret upon retrial. We affirm the trial court’s denial of defendant’s motion to preclude the State from initiating such proceedings.
Affirmed.