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In the near future, it will be essential for multimedia networks to satisfy multiple quality of service (QoS) requirements, such as bandwidth, transmission reliability, end-to-end delay etc. On the other hand, multicast technology is being increasingly used in various continuous media applications that involve video and audio. In particular, multipoint-to-multipoint communication services, including multimedia collaborations such as video conferencing and shared workspaces, will be widespread. However, when a conventional multicast routing algorithm is applied to such services it may result in traffic concentration on some links. Therefore, we propose a new multipoint-to-multipoint routing method based on the Fallback+ algorithm, which can satisfy multiple QoS requirements and avoid traffic concentrations. Finally, simulation experiments show that this method results in improved traffic load balance and efficient use of network resources.