An algorithm for solving the open-loop optimal control problem proposed by Y. Sakawa and Y. Shindo is analysed. The algorithm is essentially based on the use of the Pontriagin maximum principle. The convergence properties of the algorithm are investigated. It is established here, under weaker assumptions, that i) the algorithm is well-defined, ii) the cost functional monotonically decreases, iii) a weak necessary optimality condition is asymptotically verified, if the sequence of computational control parameters is bounded from above and from below.