Abstract: According to the matrix disturbance theory,a stability index of stochastic disturbance of meteorological field series is presented by using the norm of matrix and then the stability index is applied to l estimate indirectly the stability of EOFs.It is shown that the higher the correlation of the meteorological field series,the smaller the sample it needs to reach stability correlation structure by means of the theoritical derivation and numerical experiment and case calculation.As soon as a meteorological field series satisfied above,the more stable EOFs is obtained and vice versa.The regularity depends directly upon the sample length n and the number of stations p.For different meteorological field series there are different criterion values of sample length which satisfies the stable EOFs,thus it must be on guard against the instability of EOFs when expansion.