Envelope analysis is widely used in fault diagnosis of rolling element bearings (REBs). In envelope analysis, it is necessary to select a frequency band which is related to the resonance of the bearing. Spectral kurtosis (SK) is known as a powerful method to find the resonance band in vibration of a defective REB. SK, calculated by short time Fourier transform, suffers from its dependency on the window length. In this article, a special wavelet transform is used to obtain a SK diagram. It is shown that choice of mother wavelet function has great influence on the resulting SK diagram. The proposed wavelet is based on the impulse response of a damped single degree of freedom system. An optimization algorithm is used to optimize the SK diagram for fault detection. The method is tested for both simulated and experimental vibration data.