A silica-based coating film on a substrate surface is prepared by forming a reaction mixture comprising a tetraalkoxysilicon compound (A) and/or an alkyl/alkoxy silane compound (B), an alcohol (C), and oxalic acid (D), in such ratios that the amount of alcohol (C) ranges from 0.5 to 100 mols per mol of all alkoxy groups present in the silicon compounds (A) and (B), and the amount of oxalic acid (D) ranges from 0.2 to 2 mols per mol of all alkoxy groups in the silicon compounds (A) and (B), and while maintaining the mixture at a SiO.sub.2 concentration ranging from 0.5 to 11%, as calculated from silicon atoms in the mixture, by means of the alcohol (C); heating the reaction mixture at a temperature ranging from 50 to 180.degree. C. until the total remaining amount of the silicon compounds (A) and (B) in the reaction mixture is not more than 5 mol %, to form a solution of a polysiloxane having a number average molecular weight, calculated on the basis of a polystyrene standard, ranging from 2,000 to 15,000; applying a coating fluid containing the solution of the polysiloxane onto a substrate surface; and thermally curing a coating film obtained by the application, at a temperature ranging from 80 to 600.degree. C.