The justices rejected a petition from a Texas death row inmate without comment.
Larry Ray Swearingen was convicted of the 2000 murder of Melissa Trotter, 19, of Montgomery County, Texas. The community college student's body, strangled and her throat cut, was found in the Sam Houston National Forest.
Swearingen was convicted on a wealth of circumstantial evidence and sentenced to death. But he contended new examination of tissue samples show the young woman died while he was jailed on unrelated traffic charges. Texas strongly disputed that interpretation.
Swearingen was scheduled to be executed three times, the last time in August, before being granted stays.
The U.S. Supreme Court ruled 6-3 in 1993's Herrera vs. Collins, another Texas death penalty case, that a simple claim of actual innocence did not entitle a death row inmate to federal constitutional review despite the Eighth Amendment's ban on cruel and unusual punishments.