To improve the surface smoothness of a thin-sheet glass substrate and to ameliorate its quality by measuring the star-shaped patch as a local recess with a specified quality evaluation method and imparting the surface smoothness with the inclination within a specified range to the substrate surface.

The polishing soln. used in polishing the surface of a glass substrate is composed mainly of an abrasive, a pH regulator and water. The pH regulator is added to keep the polishing soln. always neutral not to lower the polishing efficiency, and a mineral acid such as sulfuric acid is used. The polished glass substrate is vertically erected in parallel with a screen, the polished face is irradiated with a mercury lamp, and the state of the substrate face is observed. The substrate is gradually rotated around its vertical axis, the angle (inclination) between the substrate and beam vertically projected on the screen is measured when the star-shaped patch is observed on the screen, and the substrate is accepted when the angle is 17-25°.