The invention pertains to a method and device for machining a workpiece (2), which rotates about a central axis (1) by means of a tool (3), which contains at least one planar cutting plate (17) arranged in an inclined plane (E) relative to the central axis (1) of the workpiece (2) and is provided with a curved cutting edge (21) directed toward the workpiece (2), wherein the tool (3) is non-rotatably held during the machining, and wherein the workpiece (2) and the tool (3) are displaced relative to one another along two mutually perpendicular axes (X-axis, Y-axis) within a plane (X-Y plane) that lies perpendicular to the central axis (1) of the workpiece (2) such that the point of action between the cutting plate (17) and the workpiece (2) travels along the cutting edge (21).