Abstract: In this paper the quantitative rules of error transfer and change of Gaussian integral function Fm(z) sequence calculation by recurrence formula in ab initio method are expounded. The optimal scheme of Fm(z) integral sequence calculations by conbination of upward with downward recurrence is proposed. This method assures that the absolute derivations only decrease without increasing in recurrence process, and hence the subsidiary precision prescrible is not need for the recurrence founda-tional term. As a result it can be applied to improvement of the exsitent serious Fm(z) computer programs. Combination of this method with Schaad's formula being used to p,d,f type Gaussian function calculations, the additive operation and the multiplication and exponential operation decrease by above 40% and above 60% specifically.