Some convergence properties of the projection and contraction method are proven in solving the variational inequality problem of finding a vector \(x^*\) of a convex closed set \(K\subseteq \mathbb{R}^n\) such that \(\langle f(x^*), x-x^* \rangle\geq 0\) for all \(x\in K\), where \(f\) is a continuous vector function from \(R^n\) to itself. In one of the variants of the method, when a nondegenerate solution is obtained, the entire optimal face can be identified after a finite number of iterations.