In order to eliminate the influence of the non-linear phase resulted from the non-symmetry of orthogonal wavelet on decomposition result, on the basis of zero phase filtering principle and the Undecimated Discrete Wavelet Transform (UDWT), we proposed a UDWT decomposition algorithm with zero phase characteristics, called Zero Phase UDWT (ZPUDWT).The new method can not only overcome the defects of Mallat algorithm, such as overlap of frequency and shift variance, which are caused by down sampling, but also eliminate the displacement and distortion phenomenon in decomposition results of conventional wavelet transform.Therefore, ZPUDWT is very suitable for weak feature extraction.Analysis of an example for weak feature extraction of bearings proved the effectiveness and advantages of the new method.