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An effective group key agreement protocol is important for group-oriented applications. Some key tree approaches have been proposed by other researchers. The rekey cost of some of them scales with the logarithm of the group size for a join or leaving request, in which TGDH (tree based group Diffie-Hellman) is considered as one of the most effective and secure protocols. But the rekey cost is still considerable when the group size is very large and with nodes' frequent joining and leaving (churn problem). In this paper, we present a novel group key agreement protocol KAP-AOT improved on TGDH protocol. Our protocol takes nodes' average online time into consideration and is proved to be able to further reduce computation overhead of the rekey process.