Abstract: Due to the fact that single direction and step length methods for solving some iterative methods has a single correction which might fail during the iterative process. For this and other possible reasons a double direction and step length method for solving system of nonlinear equations is presented. The method used a specific technique with two direction vectors and two step length parameters. The approximation to the Jacobian matrix is achieved by a properly derived acceleration parameter. Moreover, the normed descent line search procedure is employed in this work in order to obtain the optimal step lengths. The numerical experiment shown in this paper, depicts the efficiency of the proposed method. Mathematics Subject Classification: 65H11, 65K05, 65H12, 65H18