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In this letter, we propose a decentralized group key management algorithm called DECLKH, which combines the logical key hierarchy (LKH) and the tree-based group Diffie- Hellman (TGDH) schemes. LKH is a centralized key distribution scheme, and thus, lacks fault-tolerance. On the other hand, TGDH is relatively inferior in terms of performance to LKH although it is fault-tolerant. The proposed algorithm, DECLKH, solves the single point of failure problems of LKH with much more enhanced performance than TGDH.