This paper presents a robust and reliable offline method for induction machine's rotor fault diagnosis, under low load conditions. This method is based on the analysis in frequency domain of the stator current envelope extracted by Hilbert transform. The proposed method, which is one of various demodulation techniques, is theoretically presented then experimentally validated by testing three different induction motors: one in a healthy condition, the second with one broken bar and the third with two broken bars. Each motor is subjected to three load conditions and supplied by voltage inverter which operates at different frequencies. The main results obtained by spectrum analysis of the stator current envelope are compared with these of the traditional MCSA method. The proposed method can successfully detect the fault under various operational situations, even for the lightly load, which makes it more suitable for induction motor fault diagnosis.