The Supreme Court announced yesterday that it will reconsider the rules for permitting appeals by death row inmates who claim they have been wrongly convicted, in the case of a death row inmate who says DNA evidence proves he did not commit the crime of which he was found guilty in 1985.

Separately, just a day after its split rulings on the public display of the Ten Commandments in government buildings, the justices declined to hear four additional cases in which lower courts had struck down displays in public school classrooms, on school property and in an Ohio state judge's courtroom.

The death penalty case, House v. Bell, No. 04-8990, brings the court face to face with an issue that has shadowed the administration of capital punishment in recent years: the possibility that an innocent person could be executed.

Paul G. House is seeking release from Tennessee's death row because of what his appeal petition to the court calls "powerful new evidence of innocence."

He says that DNA tests show that the semen found on murder victim Carolyn Muncey's clothes belonged to her husband, Hubert Muncey, and not to House, as a jury in Union County, Tenn., found 20 years ago.

The issue before the Supreme Court, however, is not whether House is guilty, but how strong his case for innocence must be to win a new hearing in federal court.

The court has never quite said it is unconstitutional to execute an innocent person.

Instead, in a 1993 case, Herrera v. Collins, the court, in a 5 to 4 opinion written by Chief Justice William H. Rehnquist, said that Leonel Torres Herrera had no right to reopen his case 10 years after conviction, based solely on a claim of new proof of innocence. Justices Sandra Day O'Connor and Anthony M. Kennedy joined that opinion with the proviso that they saw little doubt of Herrera's guilt.

In 1995, however, the court ruled 6 to 3 in the case of Schlup v. Delo that a convicted murderer who had other constitutional claims in addition to an actual innocence claim could get a new hearing even after exhausting all otherwise permitted opportunities, if he could show new evidence that makes it probable "no reasonable juror would have found him guilty beyond a reasonable doubt." O'Connor and Kennedy joined that ruling, which was written by Justice John Paul Stevens.

Last year, the full 14-judge U.S. Court of Appeals for the 6th Circuit voted 8 to 6 that House's evidence did not meet this standard.

Citing the 6th Circuit majority opinion, Tennessee said in its Supreme Court brief that the evidence presented by House, "far from demonstrating his actual innocence, was countered and undermined in virtually every respect by opposing evidence presented by the State" during his federal appeal.

The Ten Commandments cases turned down by the court yesterday had been held for consideration until the court finished weighing the display of the commandments in two different public settings -- framed copies on the wall of Kentucky courthouses and a six-foot granite monument on the Texas Capitol grounds in Austin.

The Supreme Court's decision not to hear the cases is not a ruling on their merits, but it strongly suggests that the court feels the lower court rulings were at least consistent with the court's decisions on Monday.

In all four cases the court refused to review, the displays were ruled unconstitutional by the U.S. Court of Appeals for the 6th Circuit.

Two cases, Johnson v. Baker, No. 03-1661, and Adams Cty./Ohio Valley School Bd. v. Baker, No. 04-65, involved the placing of Ten Commandments monuments on the front lawns of four new high schools in Adams County, Ohio. A third, Harlan County v. ACLU, No. 03-1698, involved the posting of a Ten Commandments-centered display in Harlan County, Ky., school classrooms.

The fourth, DeWeese v. ACLU of Ohio, No. 04-841, involved a poster of the Ten Commandments in the court of Judge James DeWeese.