It is assumed that the decomposable system of nonlinear equations has a part which can be solved easily with some known methods. The proposed iterative method is such that, starting from an arbitrary point, it produces a sequence of points which converges to the solution of the initial system with right-hand side modified with the current value of the remaining part of the system. Also, convergence conditions of the algorithm are delivered. As applications, fixed-point problems and a zero-one equation are mentioned.