To improve the working accuracy of an angular part, by mounting a grinding means which comprises a grinding wheel which is brought into contact with each angular part of a square glass plate horizontally placed and fixed after the positioning, and which is horizontally rotated.

The positioning of a glass plate is performed by bringing the same into contact with all of the stoppers 4a, 4a mounted on one edge side of a positioning table 3, and the side edge stoppers 4b, 4b. Then, an elevating cylinder 11 is operated to lower a pressure member 12, to press and fix an almost central part of the glass plate from an upper part thereof. The opening parts of grinding wheels 31 respectively having an U-shaped section, and horizontally rotated at a high speed, are brought into contact with four corners of the square glass plate which is horizontally placed and fixed, for almost simultaneously grinding and polishing four angular parts of the glass plate. Further, the grinding wheel 31 is movable in the X, Y axial directions, so that each angular part of the glass plate can be circularly grinded when observed in a plane view.