Image filtering is widely used for noise reduction. It's an important preprocessing step in Magnetic Resonance Imaging (MRI) progressing. However, most noise suppression filters have the undesirable side effect of blurring edges. This paper presents a filtering method in which image pixels are treated differently according to whether they are on edges or not. It's not only effective in noise reduction, but also in edge preserving. We call it Combining Mean-Median (CMM) filter. Experimental results show that the CMM filtering is effective for noise reduction, and it can preserve edges for possible edge-detection efforts.