In a cognitive radio network (CRN), a necessary condition for nodes to communicate with each other is that they have a rendezvous (switching to the same channel at the same time). Most of the existing rendezvous-guaranteed schemes have some undesired requirements, such as demanding role preassignment, a common control channel (CCC), or a synchronous environment. In this paper, we first define the complete rendezvous problem and then propose a staggered channel hopping scheme (SCH) to solve the complete rendezvous problem. The SCH utilizes the Chinese remainder theorem (CRT) to enable a node to have a rendezvous with any of its neighbors. We have proved the correctness of SCH through the CRT. We have also analyzed the performance of the SCH under some sample scenarios. Simulation results verify the superiority of the SCH in terms of time-to-rendezvous (TTR), standard deviation of TTR, and maximum TTR (MTTR).