In the long-term operation of any real network that supplies multicast capability, the fixed routing algorithms provide solutions that are only temporarily efficient due to dynamic nature of network environments. We study the problem of rerouting multicast traffic that meets the quality-of-service requirements of real-time, distributed multimedia applications. In particular, we assume that multicast communication depends on bounded delay along the paths from the source to each destination. We present here a technique for modifying multicast tree under end-to-end delay constraint that is cost efficient and flexibly manages load in the network. The constrained Steiner tree improvement technique in directed graphs makes use of strategy for providing end-to-end delay guarantee by apportioning it locally for each link. It has been purposely designed to meet the requirements for distributed implementation in asymmetric networks.