A process for the surface polishing of a silicon wafer, includes the successive polishing of the silicon wafer on at least two different polishing plates covered with polishing cloth, with a continuous supply of alkaline polishing abrasive with SiO.sub.2 constituents, an amount of silicon removed during the polishing on a first polishing plate being significantly higher than on a second polishing plate, with the overall amount of silicon removed not exceeding 1.5 .mu.m. A polishing abrasive (1a), then a mixture of a polishing abrasive (1b) and at least one alcohol, and finally ultrapure water (1c) are added to the first polishing plate, and a mixture of a polishing abrasive (2a) and at least one alcohol and then ultrapure water (2b) are added to the second plate.