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Efficient exploration strategy is one of essential issues in cooperative multi-agent reinforcement learning (MARL) algorithms requiring complex coordination. In this study, we introduce a new exploration method with the strangeness that can be easily incorporated into any centralized training and decentralized execution (CTDE)-based MARL algorithms. The strangeness refers to the degree of unfamiliarity of the observations that an agent visits. In order to give the observation strangeness a global perspective, it is also augmented with the the degree of unfamiliarity of the visited entire state. The exploration bonus is obtained from the strangeness and the proposed exploration method is not much affected by stochastic transitions commonly observed in MARL tasks. To prevent a high exploration bonus from making the MARL training insensitive to extrinsic rewards, we also propose a separate action-value function trained by both extrinsic reward and exploration bonus, on which a behavioral policy to generate transitions is designed based. It makes the CTDE-based MARL algorithms more stable when they are used with an exploration method. Through a comparative evaluation in didactic examples and the StarCraft Multi-Agent Challenge, we show that the proposed exploration method achieves significant performance improvement in the CTDE-based MARL algorithms.