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An empirical AM/FM (amplitude modulation and frequency modulation) demodulation for computing the instantaneous frequency of an intrinsic mode function produced by the empirical mode decomposition has been proposed by Huang and his coworkers. This method totally eschews the Hilbert transform and can compute the instantaneous frequency of an intrinsic mode function very accurately. However, this paper show that the empirical FM part extracted through the empirical AM/FM demodulation may contain riding waves and is no longer an intrinsic mode function. That will make the instantaneous frequency nonsensical. To overcome this drawback, an improved method called riding wave turnover-empirical AM/FM demodulation is proposed in this paper. Experiments show very favorable results.