Abstract: The invention relates to a method of dressing both the face and the roundings on a grindstone (4) in a cylindrical grinding machine in one uninterrupted operation. The dressing device includes a pivotably disposed dressing arm (2) mounted in a carriage guide (5, 25) with ball or roller bearings (28). The diamond tip (3), which is mounted on the dressing arm (2), is traversed across the face of the stone (4) by means of a hydraulic cylinder (13) and a connecting rod (16) with a rack and pinion (11, 10). Also connected to the rod (16) is a centering cylinder (14) with a connecting rod (18) and a rack and pinion (12, 10). The rods are driven by two hydraulic motors which can cause linear or turning motion of the carriage. The second motor (14) acts as a damper during turning to insure a smooth transition throughout the curvature.