The invention concerns a cremation method carried out in an incinerator (1) in whose wall a burner (5, 6) is disposed. Combustion occurs in the incinerator (1) without natural air. At least half of the flue gases leaving the incinerator (1) are fed back uncooled to the incinerator (1) again such that these flue gases are circulated. Pure oxygen is added (9, 14) to at least some of the circulating flue gases.