This paper addresses the challenge of designing provably safe conflict-resolution procedures (CRPs) that are decentralized and decoupled from each other. The main contribution of this paper is identifying necessary and sufficient conditions to decouple CRPs. Additionally, this paper demonstrates the existence of decentralized en-route CRPs that satisfy the identified decoupling conditions for each local conflict and, thereby, guarantee global conflict resolution. An advantage of the proposed CRPs is that they do not require a reduction in the aircraft flow levels in the intersecting routes for conflict resolution, which can aid in increasing the efficiency of en-route air traffic control.