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Fault diagnosis of electrical machines based on frequency analysis of stator current has been the interest of many researchers for the past twenty years. Several frequency estimation techniques have been developed and are used to help the induction machine fault detection and diagnosis and it is still necessary to test new methods. This paper presents a technique to improve the diagnosis by using the well known MUSIC (multiple signal classification) method. This method is a powerful tool extracting meaningful frequencies from the signal and it has been largely used in different areas included electrical machines. In this application, fault sensitive frequencies have to be found in both the stator current and the stray flux signatures. They are often numerous in a given frequency range and they are affected by the signal-to-noise ratio. Then, the MUSIC method takes a long computation time to find more frequencies by increasing the order of the frequency signal dimension. To solve this problem, an algorithm based on zooming in a specific frequency range is proposed with MUSIC in order to improve the diagnosis performances to extract frequencies. The proposed method has been applied to detect incipient broken bar rotor fault in a three-phase squirrel-cage induction machine.