Michael Render appeals the district court’s denial of his petition for a writ of habeas corpus, pursuant to 28 U.S.C. § 2254 of the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA). Render argues that the state trial court violated his constitutional rights by not sufficiently inquiring into a juror who stated she felt ill before taking the verdict in his original trial. After review, 1 we affirm the district court. 2

I.

In 1990, Michael Render was charged with one count of attempted first-degree murder, one count of robbery, two counts *824 of armed burglary, and one count of unlawful possession of a firearm while engaged in a criminal offense. In 1992, Render' was convicted on the first four counts. As a habitual offender, the state court sentenced him to a term of natural life imprisonment on each of the four counts, set to run concurrently.

During the trial that led to his conviction, a juror felt ill and asked to be excused. The state court and attorneys discussed available options and instructed the bailiff to inquire about the nature of the juror’s illness. When the bailiff returned from attempting to retrieve the jury, he noted that the jury foreman had asked for a little more time. Shortly thereafter, the jury returned, indicating it had reached a verdict.

Render argued that the court should not proceed given the ill juror’s request. The state court, however, decided to accept the verdict and poll the jury afterwards. After announcing the guilty verdict, the jury was polled and confirmed that the verdict was supported by each member, including the ill juror.

II.

In his petition for a writ of habeas corpus before this Court, Render argues that the state court committed constitutional error in failing to hold a hearing to determine whether the ill juror should have been retained. According to Render, federal law 3 requires courts to inquire into a juror’s illness. Additionally, Render argues that prejudice should be assumed because the verdict was rendered soon after the ill juror asked to be excused. In Render’s view, the close proximity in time between the verdict and the ill juror’s request demonstrates the juror was forced to surrender her honest belief in Render’s innocence.

We disagree. Habeas corpus relief “is a guard against extreme malfunctions in the state criminal justice system, not a substitute for ordinary error correction through appeal.” Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 786, 178 L.Ed.2d 624 (2011) (internal quotation marks omitted). Under § 2254(d)(1) of AEDPA, the petitioner must prove that a state court adjudicated the merits of his claim in a manner that was “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 4 28 U.S.C. § 2254(d)(1); see also Woodford v. Visciotti, 537 U.S. 19, 24, 123 S.Ct. 357, 360, 154 L.Ed.2d 279 (2002) (per curiam) (establishing that petitioner carries the burden of proof for habeas claims brought under 28 U.S.C. § 2254(d)).

*825 First, § 2254(d)(l)’s phrase “clearly established Federal law” refers to Supreme Court holdings that were in effect at the time of the relevant state court decision. Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 1523, 146 L.Ed.2d 389 (2000). A state court’s decision is “contrary to” clearly established federal law, only when it either (1) applies a rule “that contradicts the governing law set forth by Supreme Court case law,” or (2) reaches a different result from the Supreme Court “when faced with materially indistinguishable facts.” Ward v. Hall, 592 F.3d 1144, 1155 (11th Cir.) (internal quotation marks omitted), ce rt. denied, Hall v. Ward, — U.S. -, 131 S.Ct. 647, 178 L.Ed.2d 513 (2010).

Second, under § 2254(d)(1), an “unreasonable application of ... Federal law” occurs (1) when the state court’s decision does not square with Supreme Court rulings on “materially indistinguishable facts,” Williams, 529 U.S. at 413, or (2) or when the state court “unreasonably extends or fails to extend a clearly established legal principle to a new context,” Ward, 592 F.3d at 1155 (internal quotation marks omitted). An application of federal law is not unreasonable simply because an appellate court thinks it incorrect or erroneous. Id. Rather, an unreasonable application must be “objectively unreasonable,” Williams, 529 U.S. at 409, such that there is “no possibility fairminded jurists could disagree that the state court’s decision conflicts with [the Supreme] Court’s precedents,” Harrington, 131 S.Ct. at 786.

Here, Render has not met the requirements for habeas relief articulated in 28 U.S.C. § 2254(d). First, the state court did not violate “clearly established Federal law.” When the jury convicted Render in 1992, Supreme Court precedent did not clearly require an inquiry into the juror’s illness beyond that which the state court performed. Hence, the state court did not violate “clearly established Federal law” on that issue. See, e.g., Anderson v. Sec’y Dep’t of Corr., 462 F.3d 1319, 1327-28 (11th Cir. 2006).

Render, however, argues that this Court’s decision in Green v. Zant established clear federal law requiring the state court to determine in greater depth whether the ill juror could continue. In Green, a state trial court discharged and replaced a juror without inquiry three hours into jury deliberations when she fell to the floor and repeatedly cried, “I can’t do it.” Green v. Zant, 715 F.2d 551, 554-56 (11th Cir. 1983). We vacated the district court’s denial of habeas relief and remanded for the purpose of conducting an evidentiary hearing on whether the juror had been capable of continuing prior to her dismissal. Id. at 555-59. But in concluding that a hearing on remand was appropriate, Green did not articulate a principle of federal law requiring state courts to conduct searching inquiry into the capabilities of jurors who wish to be excused. Rather, Green held that substitution of a juror during deliberations, if done for improper reasons, may constitute a due process violation. Id. Thus, Render’s reliance on Green is misplaced. Because no potentially improper juror substitution occurred in Render’s case, the state court did not violate “clearly established Federal law” within the meaning of § 2254(d).

Second, the state court did not “unreasonably apply” federal law as it stood in 1992. The state court instructed the bailiff to ask members of the jury whether they were capable of proceeding. They were. The state court also polled the jury after the verdict was announced to ensure each member stood by the verdict. They did. Federal law, as it existed in 1992, did not demand a specific or more elaborate type of inquiry in order to retain a juror under *826 these circumstances. Cf. Green, 715 F.2d at 556 (“Where the disability of the juror is less certain or obvious ... some hearing or inquiry into the situation is appropriate to the proper exercise of judicial discretion.” (emphasis added)). The record shows that the state court conscientiously inquired into the capacities and convictions of all members of the jury, and thus did not unreasonably apply federal law in Render’s 1992 trial. Accordingly, we affirm.

III.

The district court’s decision denying Render’s petition for habeas corpus is affirmed.

AFFIRMED.