The paper develops a finite iterative method for solving a Boolean programming problem which has been proposed earlier by the author together with J. A. Babaev and K. Sh. K. Mamedov. An iteration of this method consists of solving a similar problem with two constraints on the set of variables. In this article the author improves the algorithm by means of reducing the number of iterations. It is necessary to note that the main result which provides an estimate for the number of iterations is given without proof.