To provide a method for the production of a flame resistant fiber capable of mass-production of flame resistant fibers having a high quality by baking the fiber bundle of carbon fiber precursors having a high total denier allowing mass-production of carbon fibers.

This production of a flame resistant fiber is to introduce the fiber bundle of a carbon fiber precursor having 3,000-26,667 tex total denier D into a heating furnace by using a grooved roll having a groove pitch P (mm) in the range expressed by 9 D/11,000≤P≤9 D/3,667 and heat treating the fiber bundle in an oxidative atmosphere of a convective heating type.