Abstract: An approach for constructing one-dimensional two-channel and two-dimensional four-channel morphological wavelet with updating adaptation is presented. In the updating lifting step, selecting these points as the low-frequency signals from the 1×3 or 2×2 local windows, which absolute values of local average difference are maximum, and make the update operators possess the adaptation. Experimental results show that the low-frequency signals have the higher definition and can keep the detail information of original images well when the images are decomposed with the presented morphological wavelet.