In a recent paper Davidchack and Lai [2001], proposed the DL method as an alternative to the deficiencies presented by the Newton method for finding period-p points of dynamical systems, when the value of p increases. This article presents a theoretical and numerical study of the performance of this method for solving any nonlinear system of equations. Theoretically, it is presented the local convergence analysis of method using common hypothesis in the analysis of Newton-type methods. Numerically, it is proposed a particular election of the parameter which is applied to an example. Some numerical tests using increasing values of parameter and four test function proposed in [Lukoan, L.,1998] complete this work.