The state Supreme Court ordered a trial judge to hold a hearing into Amos King's request for new attorneys.
King, 47, filed a handwritten request for new lawyers Tuesday, accusing his current lawyers of being "pro-state" and failing to use new evidence he gave them. The lawyers refused to comment on the accusations.
Circuit Judge Susan Schaeffer scheduled a hearing Friday to consider King's request.
King is scheduled to be executed Jan. 24 for the murder of Natalie Brady, a 68-year-old widow who was raped, choked and stabbed in her Tarpon Springs home on March 18, 1977.
Schaeffer denied King's latest appeal after a hearing Tuesday and the Supreme Court will listen to oral arguments next Tuesday.
King is one of the veterans on Florida's death row; only about a dozen of the 372 people on death row have been there longer.
Florida has two other executions scheduled the first week of February.