This paper proposes an improved rotor fault detection algorithm. The main objects are: First, ameliorate the reliability of the rotor fault detection task especially under very low load in the presence of industrial frequency inverter. Second, allow even relatively unskilled users to make an automatic, fast and reliable decision on machine health with low requirements. Basing on the concept of multiple signature processing, the proposed algorithm uses Relative Harmonic Indexes (RHI) as a new fault indicator. The RHI are computed starting from many harmonics selected carefully according to their sensitivity to the occurrence of rotor bar faults, this represents its main advantage compared to the classical fault indicators which use only one or two fault signatures leading commonly to erroneous diagnosis especially under low load. The proposed algorithm requires only the stator current signal. For each data acquisition, the algorithm computes, normalises and classifies the RHI then it displays the obtained results in a simple manner. Extensive experimental tests, carried out on a 3 kW squirrel cage induction motor fed from an industrial frequency inverter, confirm the effectiveness of the proposed algorithm in detecting of rotor bar fault under different operation conditions even with very low loads.