Achieving a precise fault diagnosis for rolling bearings under variable conditions is a problematic challenge. In order to enhance the classification and achieves a higher precision for diagnosing rolling bearing degradation, a hybrid method is proposed. The method combines wavelet packet transform, singular value decomposition and support vector machine. The first step of the method is the decomposition of the signal using wavelet packet transform and then instantaneous amplitudes and energy are computed for each component. The Second step is to apply the singular value decomposition to the matrix constructed by the instantaneous amplitudes and energy in order to reduce the matrix dimension and obtaining the fault feature unaffected by the operating condition. The features extracted by singular value decomposition are then used as an input to the support vector machine in order to recognize the fault mode of rolling bearings. The method is applied to a bearing with faults created using electro-discharge machining under laboratory conditions. Test results show that the proposed methodology is effective to classify rolling bearing faults with high accuracy.