A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps : first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions resulting from the tentative splits and, third, a formula for determining the nodes levels of the resulting dendrogram. A number of such algorithms is given. These algorithms are compared using the Goodman-Kruskal correlation coefficient. As a global criterion it is an internal goodness-of-fit measure based on the set order induced by the hierarchy compared to the order associated to the given dissimilarities. Applied to a hundred of random data tables, these comparisons are in favor of two methods based on unusual ratio-type formulas for the splitting procedures, namely the Silhouette criterion and Dunn's criterion. These two criteria take into account both the within cluster and the between cluster mean dissimilarity. In general the results of these two algorithms are better than the classical Agglomerative Average Link method.