A crematorium furnace (10), comprising a primary combustion chamber (14) provided with a door (12) for introducing a coffin (34), a secondary combustion chamber (18) connected to the primary chamber (14), at least one primary burner (16) associated with the primary chamber (14), at least one secondary burner (20) associated with the secondary chamber (18), a cremation hearth (22), and a stack (26), and further comprising first injection means (27), adapted to introduce a gaseous oxidizing agent comprising oxygen directly inside the coffin (34), and ignition means (29), adapted to trigger a combustion process inside the coffin (34).