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Bipartite graphs are powerful data structures to model interactions between two types of nodes, which have been used in a variety of applications, such as recommender systems, information retrieval, and drug discovery. A fundamental challenge for bipartite graphs is how to learn informative node embeddings. Despite the success of recent self-supervised learning methods on bipartite graphs, their objectives are discriminating instance-wise positive and negative node pairs, which could contain cluster-level errors. In this paper, we introduce a novel co-cluster infomax (COIN) framework, which captures the cluster-level information by maximizing the mutual information of co-clusters. Different from previous infomax methods which estimate mutual information by neural networks, COIN could easily calculate mutual information. Besides, COIN is an end-to-end coclustering method which can be trained jointly with other objective functions and optimized via back-propagation. Furthermore, we also provide theoretical analysis for COIN. We theoretically prove that COIN is able to effectively increase the mutual information of node embeddings and COIN is upper-bounded by the prior distributions of nodes. We extensively evaluate the proposed COIN framework on various benchmark datasets and tasks to demonstrate the effectiveness of COIN.