An efficient four-step method for solving nonlinear system

In this paper, we suggest a ninth order convergence four-step method to solve system of nonlinear equations. Every iteration of the method requires three function evaluations, two first Fr\ {e}chet derivative evaluations and two matrix inversions. Hence, the efficiency index is $9^{1/(3n+6n^2+\frac{4}{3}n^3)}$, which is better than that of other four-step methods