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In ad-hoc networks, mobile nodes cannot be supported the group authentication by Internet infrastructure. To resolve the group authentication in ad-hoc networks, several protocols for group key agreement have been proposed. These protocols assumes the reliable communication links between MNs. However, wireless links in ad-hoc network are inherently unreliable. We propose a group key agreement algorithm based on hyper-cube key agreement scheme to cope with failed links during group key agreement. When a link failure occurs in hyper-cube key agreement scheme, the key agreement keeps up the process no longer. The algorithm deals with any single link failures on any one plane of a hyper-cube.