Indices of phylogenetic diversity defined on phylogenetic tree, including Daniel Faith's original definition of phylogenetic diversity index (Faith 1992), are briefly reviewed. The subtree that minimally covers a subset of terminal nodes (OTU's) with their associated internal branches has no explicit reference to the root of the full tree. The Gromov transform of phylogenetic diversity index is proposed which is defined for any triplet (x, y, r) such that x and y are terminal OTU's and r is the root of the full tree. Several properties of the transformed index are discussed. Our new software for estimating large-scale molecular phylogenetic trees implements the function of calculating this new index.