In order to solve some special classes of nonlinear systems of equations the Modified Accelerated Overrelaxation - Newton (MAORN) method, introduced in [1], is used. The same nonlinear systems have been considered by Chernyak, [5]. For their numerical solution he has used the AORN (Accelerated Overrelaxation - Newton) method. By using a similar technique as in Chernyak’s papers [4] and [5], some sufficient conditions are obtained for the global convergence. The modified method and the convergence result are simpler than the ones from [5].