The problem of optimizing the sequential algorithm for the Boltzmann machine (BM) is addressed. A solution that is based on the locality properties of the algorithm and makes possible the efficient computation of the cost difference between two configurations is presented. Since the algorithm performance depends on the number of accepted state transitions in the annealing process, a theoretical procedure is formulated to estimate the acceptance probability of a state transition. In addition, experimental data are provided on a well-known optimization problem travelling salesman problem to have a numerical verification of the theory, and to show that the proposed solution obtains a speedup between 3 and 4 in comparison with the traditional algorithm.