Faryion Wardrip's attorney claims his client did not receive a fair sentencing trial.
Wardrip has admitted to killing at least five young Texoma women in the 1980.
He was sentenced to death in 1999, and also received three life sentences.
Wardrip's appellate attorney is trying to appeal the death sentence because of what he calls ineffective representation by his public defender.
He argues Wardrip would not have been sentenced to death if his attorney had presented evidence about his clean prison record and his behavior after he was released on parole for the 1986 murder of Tina Kimbrew.
No action was taken at today's hearing and no future court dates have been set.
A federal judge previously denied the motion for an evidentiary hearing in this case.