A method of forming on a substrate an amorphous silica-based coating film having a low dielectric constant of 3.0 or below and a film strength (Young's modulus) of 3.0 GPa or more, which comprises, as a typical one, the steps of; (a) coating on the substrate a liquid composition containing hydrolysate of an organic silicon compound or compounds hydrolyzed in the presence of tetraalkylammonium hydroxide (TAAOH); (b) setting the substrate in a chamber and then drying a coating film formed on the substrate at a temperature in the range from 25 to 340° C.; (c) heating the coating film at a temperature in the range from 105 to 450° C. with introduction of a superheated steam having such a temperature into the chamber, and (d) curing the coating film at a temperature in the range from 350 to 450° C. with introduction of a nitrogen gas into the chamber.