In 2004, Hwang et al. proposed a group Key exchange protocol for sharing a secure Key in a group. Their protocol is an extension from the two party Key exchange protocol to the group one. Recently, Jung-San Lee et al. noted that Hwang et al. group Key exchange protocol has two security weaknesses. First, the forward secrecy is not con rmed in case that a new member joins the group and second, if a group member leaves the group, the backward secrecy is compromised. They proposed an improvement over this Key exchange protocol in order to provide both forward and backward secrecy among group members. In this paper, we propose another improvement over Lee et al. Key exchange, and we show that our Key exchange protocol not only preservers both forward and backward secrecy, but also it is more e cient than their protocol when a member leaves the group. Finally, we give a formal analysis for the correctness of the proposed protocol via Scyther model checking tool.