The most renowned method for solving nonlinear systems is the Newton’s method. Its importance is primarily theoretical while practical application involves certain problems. The method proposed in this paper is aimed at eliminating one of those problems, i.e. the need to solve the linear (Newtonian) system in each iteration. This is made possible by retaining the same matrix of the Newtonian system while modifying only the right-side vector in each iteration. The proposed method can be considered as the improvement of the fixed Newton’s method.