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The growth of the Internet inspires lots of new network applications, and many of them are based on group communication models, In this paper, we propose an approach to reduce the path length of a binary key tree managed by a centralized group key server by recomposing it, such that subsequent group operations can benefit from fewer auxiliary key updates, fewer encryptions, and less multicast bandwidth. The server can recompose the key tree in a join or a leave operation without the use of additional auxiliary keys or encryptions. An optimal composition algorithm is presented. It is shown in our analysis that the algorithm is effective to reduce the path length of a binary key tree in join operations and leave operations.