A new simple method for constructing a color palette that uses the radius weighted mean cut (RWM-cut) is proposed. The method is a hierarchically divisive method, and each two-class partition uses the centroid and the RWM only. Experiments show that the RWM-cut algorithm is feasible and visually acceptable. The algorithm can either be used alone or be used to create a good initial palette for the LBG algorithm. Besides the 3-D version, a 1-D version of the RWM-cut algorithm is also included in the paper for real-time color quantization. The quantization error is small and the processing speed is competitive. Dithered images are also provided.