Abstract: After a synoptical and statistical analysis1 of the 5-day's mean circulation of the 500mb surface in the area of Asia for the period of 1964-1973, the results of computation and analysis of the renewal data for the period of 1969-1978 years are given in this artical. It is pointed out that EOF is an invariant, if the original data are processed by the method of centralization fox filtering the seasonal variations. It is shown that the general condition for stability of EOF is the stability of the random process, which will be studied. Therefor, these results may give a physical fundation for the method of Long-range weather forecasting by using the technique of EOF. Some problems for the application of EOF in meteorology are also discussed in this paper. Some interesting viewpoints about the effective application of EOF are obtained.