Palette re-ordering is a well known and very effective approach for improving the compression of color-indexed images. If the spatial distribution of the indexes in the image is smooth, greater compression ratios may be obtained. As known, obtaining an optimal re-indexing scheme is not a simple problem. In this paper we provide a novel algorithm for palette re-ordering problem showing the advantages of using a neural network instead of classical heuristic methods. We propose to apply the Motor Map neural network which is considered an extension of the well-known SOM Kohonen neural network. Experiments confirm the effectiveness of the proposed technique. Categories and Subject Descriptors (according to ACM CCS): I.4.2 [Image processing and Computer Vision]: Compression (Coding)