We present the first photoelectron-photoion-photoion coincidence (PEPIPICO) spectra of ozone, O-3, excited at the O1s edge. From symmetry considerations the oxygen atoms at the end of the V-shaped molecule are chemically in-equivalent to the central oxygen atom. For the excitation from one of the terminal O1s orbitals to 7a(1)(sigma *), experiments combined with simulations yielded that photo-induced breaking of the bond closest to the core-excited terminal atom occurs in at least 70 +/- 10% of the cases. We interpret this as due to a 'memory' effect of the localized core-hole after the Auger decay. Consequently the sequential two-step model, i.e. core excitation-and-decay resulting in a state with delocalized valence holes followed by dissociation, is not adequate in this case.