Let \(R\) be a valuation ring with maximal ideal \(J\), and let \(V\) be a free \(R\)-module of finite rank \(n\) equipped with a symmetric bilinear form whose induced form on \(V/JV\) is anisotropic. The author shows that if \(\pi\) is an element of the orthogonal group of \(V\) such that the image of \(\pi^ 2-1\) is a direct summand of \(V\), then \(\pi\) is a product of two orthogonal involutions. Further, if \(n\) is odd, every orthogonal mapping of \(V\) is a product of five involutions; four suffice when \(n\) is even. A new proof of D. Ljubić’s theorem [Can. Math. Bull. 32, 54-63 (1989; Zbl 0635.51010)] on isometry group of absolute geometries is also presented.