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This paper presents a quorum-based distributed algorithm for the extended group mutual exclusion problem. In the group mutual exclusion problem, multiple processes can enter a critical section simultaneously if they belong to the same group. Processes in different groups cannot enter a critical section at the same time. In the extended group mutual exclusion, each process is a member of multiple groups at the same time. Each process can select which group it belongs at making a request. The algorithm for the group mutual exclusion cannot be applied for this extended problem, since there can be a case that two processes are prevented from entering a critical section simultaneously even when they are capable of doing so. We call the above situation unnecessary blocking. We present a quorum-based algorithm that prevents unnecessary blocking and show its correctness proof.