We present an algorithm to solve: Find (x,y) E A X A.L such that y E Tx, where A is a subspace and T is a maximal monotone operator. The algorithm is based on the proximal decomposition on the graph of a monotone operator and we show how to recover Spingarn's decom position method. We give a proof of convergence that does not use the concept of partial inverse and show how to choose a scaling factor to accelerate the convergence in the strongly monotone case. Numerical results performed on quadratic problems confirm the robust behaviour of the algorithm.