Attorneys for Robert Van Hook had argued that the lawyers who represented him during the sentencing phase of his trial failed to do an effective job.
In its ruling Monday, the high court reversed a ruling by the 6th U.S. Circuit Court of Appeals in Cincinnati.
Van Hook killed David Self in Self's apartment in Cincinnati before robbing him and fleeing to Florida, where he was arrested and confessed.
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Van Hook's lawyer Keith Yeazel says another appeal issue is pending before the 6th Circuit.
Ohio Attorney General Richard Cordray says the death sentence is appropriate due to the "horrific nature" of the crime.
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