Abstract: The principl that the molecular symmetry can be used to simplifying the calculations of a vast amount of many-center integrals by other workers has been proved with mathematical method. The method with which the local symmetry of a molecule is also used to simplify this sort of evaluations has been put into effect on MQAB 80 ab initio program. Having qualities of covenient and effective, the sample calculations being performed show that this method can save the CPUtime up to 50% or even more.