As a continuation work following [4] and [5], a new ABS-type algorithm for a nonlinear system of equations is proposed. A major iteration of this algorithm requiresncomponent evaluations and only one gradient evaluation. We prove that the algorithm is superlinearly convergent withR-order at least τn, where τnis the unique positive root ofτn−τn−1−1=0. It is shown that the new algorithm is usually more efficient than the methods of Newton, Brown and Brent, and the ABS-type algorithms in [1], [4] and [5], in the sense of some standard efficiency measure.