Seven years later, a white juror, Barney Gattie, signed an affidavit explaining his reasoning. He said he had drawn a distinction between Mr. Tharpe and his victim, both of whom were black.

“The Freemans are what I would call a nice Black family,” Mr. Gattie wrote. “In my experience I have observed that there are two types of black people. 1. Black folks and 2. Niggers.”

“Because I knew the victim and her husband’s family and knew them all to be good black folks, I felt Tharpe, who wasn’t in the ‘good’ black folks category in my book, should get the electric chair for what he did,” Mr. Gattie wrote.

“After studying the Bible,” he added, “I have wondered if black people even have souls.”

Mr. Tharpe sought to reopen his case based on the affidavit, but state and federal courts ruled against him. The United States Court of Appeals of the 11th Circuit, in Atlanta, stated that “Tharpe failed to demonstrate that Barney Gattie’s behavior ‘had substantial and injurious effect or influence in determining the jury’s verdict,’ ” quoting a Supreme Court decision.

The majority opinion on Monday said the appeals court should reconsider its decision not to hear Mr. Tharpe’s appeal. “Gattie’s remarkable affidavit — which he never retracted — presents a strong factual basis for the argument that Tharpe’s race affected Gattie’s vote for a death verdict,” the opinion said.