In order to solve the problem that fault feature cannot be effectively revealed by the Improved Envelope Spectrum via Feature Optimization-gram（IESFOgram）algorithm under the condition of the random slip of the REB. The improved version of the IESFOgram algorithm is proposed based on setting the characteristic frequency tolerance. The spectral correlation analysis tool is employed to extract the bearing fault components by the second-order cyclostationarity characteristic. Characteristic frequency tol?erance is determined by the bearing random slip，and a suitable sub-band with abundant fault information is selected by the maxi?mum value of sum of each order harmonic frequency of the characteristic frequency to the sideband integration ratio. The fault lines of faulty bearing can be effectively identified by the envelope spectrum analysis. The analysis results of simulation data，open data from Western Reserve University and experimental data show that the proposed scheme in this study can effectively solve the draw ?back of IESFOgram algorithm under the random slip of the REB condition.