The "neighbor-joining algorithm" is a recursive procedure for reconstructing trees that is based on a transformation of pairwise distances between leaves. We present a generalization of the neighbor-joining transformation, which uses estimates of phylogenetic diversity rather than pairwise distances in the tree. This leads to an improved neighbor-joining algorithm whose total running time is still polynomial in the number of taxa. On simulated data, the method outperforms other distance-based methods. We have implemented neighbor-joining for subtree weights in a program called MJOIN which is freely available under the Gnu Public License at http://bio.math.berkeley.edu/mjoin/.