Recently, with the explosive growth of communication technologies, group oriented services such as teleconferencing and multi-player games are increasing. Access to information is controlled through secret communication using a group key shared among members, so efficient updating of group keys is vital to maintaining secrecy of large and dynamic groups. In this paper, we employ (2,4)-tree as a key tree, which is a height balanced tree, to reduce the number of key updates caused by joins or leaves of members. Specifically, we use the CBT (Core Based Tree) to determine the network configuration of the group members to reflect that onto the structure of the key tree. This allows for more efficient updates of group keys when splitting or merging of subgroups occurs by network failure or recovery.