The edge region of one side of a semiconductor wafer is polished by pressing the wafer by means of a rotatable polishing head against a polishing pad lying on a rotating polishing plate, and containing fixed abrasive. The polishing head is provided with a resilient membrane radially subdivided into a plurality of chambers by gas or liquid cushions, the polishing pressure independently selectable for each chamber. The wafer is held in position during polishing by a retainer ring pressed against the polishing pad with an application pressure, a polishing agent is introduced between the wafer and the polishing pad, and the polishing pressure exerted on the wafer in a chamber lying in the edge region of the wafer of the polishing head, and the application pressure of the retainer ring, are selected so that material is essentially removed only at the edge of the wafer.