The Ninth Circuit Court of Appeals in San Francisco had issued the stay earlier Monday so they could consider whether or not to grant Cooper a new hearing on evidence that could lead to a reduced sentence.
The high court's action means the issue remains in the hands of the Ninth Circuit. The San Francisco Chronicle said the Supreme Court's decision was unanimous.
Cooper was convicted in 1985 of murdering four people in a Chino Hills home after escaping from a nearby prison. Joshua Ryen, 8, barely survived the attack that killed his parents, sister and best friend.
Gov. Arnold Schwarzenegger refused Cooper's request for clemency; however Cooper's supporters contend that new tests on evidence and new information from witnesses deserve to at least be heard before the execution is carried out.
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