Abstract: A method for deburring especially a steel strip (1) cut into slabs (1a) with the aid of an oxygen cutting torch (18) whose blast is perpendicular to one (2) of the principal faces of the strip (1). The method consists in directing, onto the principal face (3) of the strip (1) opposite the principal face (2) receiving the blast from the oxygen cutting torch (18) and in the zone for cutting up the strip (1), a blast of fluid which is inert with respect to the blast from the torch (18).