Let k be a non-finite Dedekind domain, and σ be the ring of its integers. We shall assume that the ring R = σ/ (2) is finite. Let us denote by M n (k) (resp. M n (σ) ) the ring of all n by n matrices with entries in k (resp. in σ), and G l n (k) its group of units. We denote by s l n (k) the subgroup of G l n (k) whose elements g have determinant, det g, equal to one. Let H e M n (σ) be a symmetric matrix, i.e., H = t H where t H denotes the transpose matrix of H. We let G = SO (H) = { g e S l n (k) l t gHg = H }, and we let G σ = G∩M n (σ). We want to exhibit certain H for which G σ is not maxinal in G, in the sense that there exist a subgroup Δ contains G σ properly and [Δ : G σ ] is finite.