This paper presents an algorithm, the combined Schubert/secant/finite difference algorithm, for solving sparse nonlinear systems of equations. This algorithm is based on dividing the columns of the Jacobian into two parts, and using different algorithms on each part. This algorithm incorporates advantages of both algorithms by exploiting some special structure of the Jacobian to obtain a good approximation to the Jacobian by using a little effort as possible. Kantorovich-type analysis and a locally q-superlinear convergence results for this algorithm are given.