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After loosening the hypothesis of bank size, this paper developed an improved three-bank model to analyze the relation between bank size and its systemic importance. By introducing L function, multivariate extreme theory and three indexes of banking systemic importance, the paper analyzed the impact of size on banks' systemic importance, and found that bank size is the necessary condition of the systemic importance, but not the sufficient condition. In addition, this study conducted an empirical analysis by examining the trading data of 14 listed commercial banks in China. The results were basically in accord with our theoretical prediction. Both the theory and empirical results point out that the size has played a critical role in banks' systemic importance and its impact would be weakened as soon as the size reaches some threshold. This study has theoretical and practical value for the identification and supervision of banks' systemic importance. [ABSTRACT FROM AUTHOR]