Derivative-free schemes are a class of competitive methods since they are one remedy in cases at which the computation of the Jacobian or higher order derivatives of multi-dimensional functions is difficult. This article studies a variant of Steffensen’s method with memory for tackling a nonlinear system of equations, to not only be independent of the Jacobian calculation but also to improve the computational efficiency. The analytical parts of the work are supported by several tests, including an application in mixed integral equations.