The local optimization techniques is the basis of majority of regular (exact) algorithms for the non-monoton pseudoboolean functions optimization as the most simple and, accordingly, the most universal method of the discrete optimization. However, the local optimization method does not guarantee the elimination of the total examination when the pseudoboolean optimization problem in a general state is solved. In the present paper the cutting off algorithms are suggested which guarantee the total examination elimination for any pseudoboolean optimization problem.