In this paper, an effective procedure for broken rotor bar (BRB) fault detection in a three-phase squirrel-cage induction machine (SCIM) is proposed. This approach relies on a motor current signature analysis (MCSA) by observing the specific fault-related current component generated by applying the DC injection braking method. Unlike the traditional MCSA, which is commonly focused on the detection of BRB sidebands around the fundamental current component, the proposed methodology introduces a new BRB feature in the current spectrum which makes it much easier for identification. The distinctive time-frequency evolution pattern of this feature provides the reliable identification of BRBs, even under no-load operating conditions, thus overcoming the major drawback of traditional MCSA-based methods. Fault severity classification is easily performed through the magnitude inspection of the BRB fault-related current component. In addition, the proposed approach does not require high-complexity signal processing algorithms to achieve reliable results. The proposed concept is presented theoretically, assisted by a magnetically coupled multiple circuit model of the SCIM, both with healthy and faulty rotor bars. Finally, the experimental tests validate the proposed methodology and demonstrate its effectiveness and usefulness.