A goal of a BISDN network is to provided integrated transport for a wide range of applications such as teleconferencing, Video On Demand etc. There require multipoint communications in addition to conventional point-to-point connections. Therefore multicast capabilities are very essential in multimedia communications. In this paper, we propose a new multicast cell scheduling method on the Parallel Multicast Packet Switch with Ring network: PMRN which are based on separated HOL. In this method, we place two different HOLs, one for unicast cells and the other for multicast cells. Then using non-FIFO scheduling, we can schedule both unicast cells and multicast cells which are available at the time in the input buffer. The simulation result shows that this method reduces the delay in the input buffer and increases the efficiency of both point-to-point network and ring network and finally enhances the bandwidth of the overall packet switch. A goal of a BISDN network is to provided integrated transport for a wide range of applications such as teleconferencing, Video On Demand etc. There require multipoint communications in addition to conventional point-to-point connections. Therefore multicast capabilities are very essential in multimedia communications. In this paper, we propose a new multicast cell scheduling method on the Parallel Multicast Packet Switch with Ring network: PMRN which are based on separated HOL. In this method, we place two different HOLs, one for unicast cells and the other for multicast cells. Then using non-FIFO scheduling, we can schedule both unicast cells and multicast cells which are available at the time in the input buffer. The simulation result shows that this method reduces the delay in the input buffer and increases the efficiency of both point-to-point network and ring network and finally enhances the bandwidth of the overall packet switch.