A method for chamfering the axially facing ends of toothed cylindrical or conical workpieces by pushing an effective tool into cutting engagement with said workpiece, which method includes the steps of moving said tool back and forth in response to the peripheral speed of the said workpiece which continuously rotates about its axis of rotation, engaging said tool with said workpiece during said back and forth movement for removing material from said workpiece during each stroke of said tool which is directed onto said axially facing ends of successive teeth of said workpiece, the improvement wherein said step of moving said tool back and forth includes the step of orienting a cutting edge on said tool on a circular segment, the axis of which extends parallel to a radial of said workpiece, which radial starts out from said axis of said workpiece and extends through a tooth on which machining is being performed.