As data rates are increasing continuously in wireless networks, additional ways of improving system performance and providing higher rates is needed. One scheme that has recently attracted a lot of attention, is using relays in order to provide additional diversity, especially in scenarios that use of multiple antennas may not be practical at transmit or receive sites. In this paper, we will present a novel channel assignment scheme at the relay which will provide full diversity for the case in which two non-cooperative independent users communicate with their destination through a single relay and by using only two frequency channels. As the simulation results show, through use of this approach, significant performance improvement is achieved in comparison with the case in which each user and its corresponding relay use an independent channel for transmission. In addition, the proposed scheme is applied to two main relay-based transmission systems, namely amplify and forward (AF) and decode and forward (DF). As the results show, the performance of DF algorithms is especially superior in scenarios in which the relay is closer to the receiver.