A furnace to flame-resistantly treat a precursor fiber strand by sending hot air to a heat treatment chamber through a hot air blowing nozzle in a direction parallel to a running direction of the strand is provided. The hot air passes through a porous plate and a rectifying member satisfying the following conditions: (1) A/B≧4.0; (2) 0.15≦α≦0.35; (3) 0≦B−d≦20; and (4) 80% or more of the area of one opening of the porous plate when facing surfaces of the porous plate and the rectifying member overlap is included in one opening of the rectifying member, where A is the rectifying member hot air passage distance (mm), B is a horizontal maximum distance (mm) of one opening of the rectifying member, α is a rate of hole area of the porous plate, and d is the porous plate equivalent diameter (mm).