A cutter for producing face gears, comprising a disc-shaped cutter body with cutting teeth (23) fitted on the periphery. The cutting edge (24) of each cutting tooth lies in a surface of revolution which is produced by turning an imaginary gear wheel of infinitely low thickness about the axis (20) of the cutter and simultaneously about its own axis. Each cutting tooth (23) of the cutter is of such a shape that the cutting tooth is re-grindable, without the shape of the cutting edge of the cutting tooth changing as a result. This is achieved through the fact that the profile of each cutting tooth shifts in planes (22, 22a, 22b...) from the cutting edge (24) of the cutting tooth to the rear side thereof in the direction of the axis (20) of the cutter.