According to the basic characteristic of rotor bar breaking fault in induction motors and the physical concept of Hilbert transform of sinusoidal signal， this paper presents the definition of Hilbert modulus of the filtered stator current signal of induction motors. Corresponding algorithm is given by integrating techniques of Hilbert transform， spectrum analysis/correction and self-adaptive filter perfectly. The paper reveals the rule that the area in complex plane occupied by Hilbert modulus of the filtered stator current signal can reflect whether rotor bar breaking fault occurs or not. It shows that the value of Hilbert modulus will increase with the development of this type of fault in induction motors. Results of thorough investigation based on a variety of simulation and experiment demonstrate that the revealed rule is correct. Moreover， a novel characteristic of rotor bar breaking fault is proposed， i.e. the Hilbert modulus gyration radius of the filtered stator current signal. Simulation and experiment results show that the Hilbert modulus gyration radius of the filtered stator current signal， as a characteristic of rotor bar breaking fault， is sensitive to the fault itself and robust to some extent to the load. Hence it can be used to detect rotor bar breaking fault in induction motors.