It have been one open and significant topic for real-time applications to enhance the processing-speed of Boltzmann machines for long time. One effective way of solution of this problem is the augmentation of probability of neurons' state move. In this paper, a novel method, called a rejectionless method, was proposed and introduced into the Boltzmann machines for this augmentation. This method has a feature of independence on the ratio of neurons' state move. The efficiency of this method for speed-up was confirmed with the experiments of TSP and graph problem.