Unexpected bearing failures may cause unscheduled downtime and economic losses. It is, therefore, very important to find the faults symptoms of the rolling element bearing components. Vibration signal of fault bearing is nonlinear and non-stationary in nature, which makes the stationary assumed methods not appropriate. In this paper, a biphase randomization wavelet bicoherence method is introduced, which combines benefits of the wavelet transform and the bicoherence analysis. By simultaneously using the amplitude of the continuous wavelet transform and biphase information, this method can eliminate the spurious bicoherence coming from long coherence time waves and non phase coupling waves efficiently. Based on this method, two quadratic nonlinearity features are proposed for fault diagnosis of rolling element bearing. At the same time, the proposed features are applied to the real-world vibration data collected from locomotive roller bearings with faults on inner race, outer race and rollers, respectively. Experiment results demonstrate that the performance of the proposed features is much better than that of some original features.