In this paper we introduce a new class of iterative methods for solving the monotone variational inequalities u*∈Ω, (u+u*)T F(u*)≥0, Au∈Ω Each iteration of the methods presented consists essentially only of the computation of F (u) a projection toΩ, v:= PΩ[u-F(u)], and the mapping F(v). The distance of the iterates to the solution set monotonically converges to zero. Both the methods and the convergence proof are quite simple.