2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61331It is shown that every linear surjective isometry between two right, full, Hilbert C*-modules is a sum of two maps : a (bi-) module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-) module actions. Every such isometry can be extended to an isometry of the C* linking algebras.41 pages, Latex, To appear in the Transactions of AMSOperator AlgebrasFunctional Analysis46L08; 46L07; 46B99text