# Existence of symplectic basis

Let $$R$$ be a PID and $$M$$ a free, finite rank $$R$$-module with a perfect billinear form $$\omega$$ such that $$\omega(v,v)=0$$ for all $$v \in M$$. Does anyone know a reference for the fact that a symplectic basis exists? By symplectic basis, I mean a basis $$x_1,\ldots x_n,y_1 \ldots y_n$$ of $$M$$ with $$\omega(x_i,x_j)=0$$, $$\omega(y_i,y_j)=0$$, and $$\omega(x_i,y_j)=\delta_{i,j}$$.