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A network partition, which makes it impossible for some pairs of processes to communicate with each other, is one of the most serious network failures. Although the notion of k-coterie is introduced to design a k-mutual exclusion algorithm that is robust against network failures, the number of processes allowed to simultaneously access the critical section may fatally decrease once network partition occurs. We discuss how to construct a k-coterie such that the k-mutual exclusion algorithm adopting it is robust against a network 2-partition. To this end, we introduce the notion of complemental k-coterie, and show that complemental k-coteries meet our requirements. We then give methods for constructing complemental k-coteries, and show a necessary and sufficient condition for a k-coterie to be complemental.