An identity between the hyper-Wiener index (WW) and the Wiener index (4 of a tree is deduced, showing that these two molecular-structure-descriptors are more intimately connected than earlier believed. Let T be a tree on n vertices and e be its edge. Let T-1 (e) and T-2(e) be the components of the disconnected graph obtained by deleting e from T. Then WW(T) = (n/2)W(T) - (1/2) Sigma(e) [W(T-1(e)) + W(T-2(e))] with the summation embracing all edges of T. (C) 2002 Published by Elsevier Science B.V.