We consider a decentralized similarity control problem for composite nondeterministic discrete event systems, where each subsystem has its own local specification and the entire specification is described as the synchronous composition of local specifications. We present necessary and sufficient conditions for the existence of a complete decentralized supervisor that solves a similarity control problem under the assumption that any locally uncontrollable event is not shared by other subsystems. We also show that the system controlled by the complete decentralized supervisor that consists of maximally permissive local supervisors is bisimilar to the one controlled by the maximally permissive monolithic supervisor under the same assumption.