The angular distributions of intensity of reflected radiation (ADIRR) of thin a-Si films on thick, parallel-sided transparent substrates illuminated with light beam of finite diameter were fitted with theoretical dependencies. It enabled to evaluate refractive index, absorption coefficient, thickness and its variation over illuminated thin film area, as well as the refractive index of the substrate. The parameter values obtained are consistent with those determined by standard methods. The novel ADIRR method of investigation is complementary to multiple angle reflectometry and ellipsometry techniques and can be effectively used to determine parameters of thin films that weakly absorb the used radiation.