In the present paper, at first, we propose a new two-step iterative method for solving nonlinear equations. This scheme is based on the Steffensen's method, in which the order of convergence is four. This iterative method requires only three functions evaluation in each iteration, therefore it is optimal in the sense of the Kung and Traub conjecture. Then we extend it to the method with memory, which the order of convergence is six. Finally, numerical examples indicate that the
obtained methods in terms of accuracy and computational cost are superior to the
famous forth-order methods.