A new recursive computational algorithm for evaluating the entries in the generalized block-pulse matrix is derived in this paper. The Stirling number and a new extended theorem are used to prove the constant difference property of the entries of the generalized block-pulse operational matrix. A recursive algorithm can then be obtained. The reduction of computing effort and associated errors is very significant when the number of computing intervals is realistically large. In comparison with the previous recursive algorithm for repeated integral operations, this new algorithm specifically addresses evaluation of the matrix entries, which, as is well known, can then be applied to evaluate the effect of multiple integrations without the need for repeated applications of the conventional block-pulse function.