This paper briefed the concept of annual maximum series(AMS) and annual exceedance series(AES),indicating that the use of AMS contradicts the definition of return period.Having taken the rainfall data of 1438 stations in the Southwest Semiarid area of the U.S.A(SSUS) and 96 stations in the Taihu Lake Basin(TLB) of China as examples for frequency analysis,we find out that the quantiles estimated based on AMS under current conventional computation are underestimated,especially for frequent events,by comparison of the empirical frequency of data with the theoretical exceedance probability.However,the findings for the SSUS data are more justified than those for the data in the TLB.The study suggests the possible causes for the difference could be,via a skewness analysis of AMS data in the TLB,that the stations used for the study in the TLB are very limited and data series are short in comparison with the SSUS data.Furthermore,only few high values are available in the high value interval,resulting in discontinuous AMS histograms for most stations in the TLB.