Frequency domain analysis using the Fast Fourier transform (FFT) has been a popular method for diagnosing broken rotor bar (BRB) faults in squirrel-cage induction motors (IM). However, FFT analysis is limited by sampling frequency and time acquisition constraints, making it less effective under time-varying conditions. To overcome these difficulties, a novel BRB fault detection method for non-stationary conditions is proposed. The proposed strategy is based on the recently developed robust local mean decomposition (RLMD) and Hilbert transform (HT) methods. Using these techniques, the BRB characteristic frequency and amplitude component are obtained from only one phase stator current allowing automation of the features detection process. in fact, HT is used to extract the stator current envelope (SCE). Then, the SCE is processed by RLMD for determining the sub signals production functions (PFs). Finally, HT is applied to the most sensible PF to compute its instantaneous frequency and amplitude. The tracking of the BRB fault characteristic can inform us about the condition of the induction motor. The effectiveness of the proposed diagnostic strategy is validated through simulation conducted in the Matlab environment. The simulation results show the capability of this method to track accurately the frequency and amplitude of the 2sf component where f and s represent the fundamental stator current frequency and motor slip respectively