Singular non-stable signal will occur when the rotating machinery gets some faults. Hence, it is important to detect the singularities for the condition monitoring and the fault pre-diagnosis of the machinery. Based on the partial decomposition in frequency domain, using the harmonic wavelet package method to analyze the simulated signal and diagnosis the practical rub faults of rotor, it expressed the ability of harmonic wavelet analysis on arbitrary detail of frequency section. It is shown that harmonic wavelet package method has many advantages over other wavelets. The satisfied results are received over the analysis of the practical signal. This provides a new method for fault signal analysis of rotating machinery.