Diagnosing induction motor BRB fault at an incipient level, that is, detecting a partial (half) BRB fault, is a challenging task, especially when motor is operating under light-load conditions. Several methods, including MUltiple SIgnal Classification (MUSIC), have been applied in literature for diagnosing this type of fault, especially under light-load conditions. However, this method is time-consuming, making it computationally expensive and unfeasible. Herein, we present a new algorithm that can reduce the computational time required for detecting half-BRB fault. The proposed algorithm captures the original current and modulates the same by injecting it with a high-amplitude signal of known frequency. Next, it applies Hilbert transform to extract the envelope of the mixed signal. This proposed method ultimately reduces the computational time in comparison to applying MUSIC algorithm directly. Experiments performed under both healthy and faulty conditions to demonstrate the validity of the proposed Signal Injected and Generated Hilbert (SInGH) method.