In contrast to self-assembled aggregates of conventional ionic (including polymeric) surfactants the equilibrium micelles of diblock copolymer with a pH-sensitive polyelectrolyte block can exhibit two inverse sequences of morphological transitions triggered by an increase in solution salinity. The direct sequence of the sphere-cylinder-lamella transitions is similar to that for the copolymer with a strongly dissociating ionic block and occurs at a high salt concentration in solution. The abnormal reversed sequence of the lamella-cylinder-sphere transitions is predicted to occur at relatively low ionic strength in solution. The origin of the reentrant transitions is coupling between aggregation and ionization in copolymer micelles.