Self-Organizing Maps (SOM) are very powerful tools for datamining, in particular for visualizing the distribution of the data in very highdimensional data sets. Moreover, the 2D map produced by SOM can be used for unsupervised partitioning of the original data set into categories, provided that this map is somehow adequately segmented in clusters. This is usually done either manually by visual inspection, or by applying a classical clustering technique (such as agglomerative clustering) to the set of prototypes corresponding to the map. In this paper, we present a new approach for the segmentation of Self-Organizing Maps after training, which is both very simple and efficient. Our algorithm is based on a post-processing of the U-matrix (the matrix of distances between adjacent map units), which is directly derived from an elementary image-processing technique. It is shown on some simulated data sets that our partitioning algorithm appears to give very good results in terms of segmentation quality. Preliminary results on a real data set also seem to indicate that our algorithm can produce meaningful clusters on real data.