Consider N entities to be classified, and a matrix of diffimilarities between pairs of them. The split of a cluster is the smallest dissimilarity between an entity of this cluster and an entity outside it. The Single-Linkage algorithm provides partitions into M clusters for which the smallest split is maximum. We study here the average split of the clusters or, equivalently, the sum of splits. An O(N³) algorithm is provided to determine maximum sum of splits partitions into M clusters for all M between N-1 and 2.