The research on the stability theory of fractional order nonlinear system has an important value for the application of synchronization and the control of fractional order chaotic system. The discussion that the stability discrimination of fractional order nonlinear system is converted into that of corresponding integer order nonlinear system has an important significance. In this paper, through the examples, for time-varying coefficient matrix, we point out the existing mistake of the discrimination theorem that states that if the integer system is stable, then its corresponding fractional system with order less than one is also stable. We also analyze the causes of the mistake.