A method for revamping a secondary reformer (1), the reformer comprising an internal gas riser pipe (8) for routing a process gas from a bottom gas inlet to a combustion chamber (5) located above a catalytic zone (6), and a distributor (9) for introduction of an oxidation agent such as process air into the combustion chamber. The original distributor of the oxidation agent is discontinued, the gas riser pipe is shortened (8′) and the outlet end of the shortened gas riser pipe is arranged to deliver a gas flow directed upwards. A new burner (20) is installed on top of the reformer, the new burner being arranged to deliver an oxidation agent such as process air with a downward flow, thus obtaining a counterflow mixing zone (23) and formation of a diffusion flame above the outlet end of the gas riser pipe.