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This paper introduces a new methodology for signal singularity detection based on the combination of wavelet-based Holder exponent and Hilbert transform. Firstly, a discrete wavelet-based Holder exponent function is derived, which is viewed as a discriminant power function and provides a measure of the signal's regularity at different time points. Then local minimum method of Holder exponents is introduced to select important singularity positions arranged in ascending order, this enables us to accurately determine when the singularities occur. Finally, by taking Hilbert transform, the instantaneous frequencies are computed at the selected important positions. The numerical simulation results presented herein show the proposed method can effectively detect time-frequency features of the singularity. The proposed method is more sharp and effective than by using the wavelet-based Holder exponent method alone, which can only predict when the singularities occur.