Abstract: In this paper the authors convexly combine the the descent directions of the CGD algorithm and the MPRP algorithm for solving the monotone nonlinear equations,construct the new descent direction and give the new algorithm,and give the globally convergent theorem of the new algorithm.At last the authors compare the algorithms through the numerical experiments and  find that the new algorithm is better than the original algorithms.

Key words: MPRP algorithm, CGD algorithm, convex combination, monotone nonlinear equations, global convergence