A grinding machine for grinding a workpiece comprises a machine frame, a bearing device provided on the machine frame and movable along guides, in which a cup-shaped grinding wheel is rotatably drivable about a grinding wheel axis and electrically insulated. The grinding wheel is electrically connected to a generator. The device for profile dressing, sharpening and cleaning the grinding wheel consists of a single cup-shaped electrode, which is drivable about its central axis and is placed on a slide, which allows a working gap to exist between the machining surface of the cup-shaped electrode and the annular abrasive surface. A spark erosion discharge occurs in the gap when a voltage is applied. The grinding wheel can thereby be optimally conditioned by electric discharge machining.