A new expression is found for the perturbation energy, with the principle feature that it is in remainder form. The remainder is first applied or manipulated to obtain the familiar infinite series of perturbation theory. Secondly, an iterative procedure for solving the Schrödinger equation is proposed. It is shown, by making use of the remainder, that this procedure leads to results equivalent, in the small perturbation limit, to the results of perturbation theory.