LKH (logical key hierarchy) is a basic method in secure multicast group rekeying. LKH is efficient in real time group rekeying since it does not distinguish the different probability among the group members. However when members have diverse changing probability or different changing modes, the gap between LKH and the optimal algorithm will become bigger. If the probabilities of members have been known, LKH can be improved someway, but the changing probability of members can not be known exactly. Based on the basic knowledge of group members, in R-LKH (Refined-LKH), the active members and inactive members are partitioned and set on different locations in the logical key tree firstly. Then the concept “dirty path” is introduced in order to reduce the repeated rekeying overhead in the same path. All these can decrease the number of encryption in group manager and the network communication overhead. The simulation result indicate that R-LKH has a better improvement over LKH if the multicast group members’ behavior could be distinguished “approximately”.