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Due to the partial observability and communication constraints in many multi-agent reinforcement learning (MARL) tasks, centralized training with decentralized execution (CTDE) has become one of the most widely used MARL paradigms. In CTDE, centralized information is dedicated to learning the allocation of the team reward with a mixing network, while the learning of individual Q-values is usually based on local observations. The insufficient utility of global observation will degrade performance in challenging environments. To this end, this work proposes a novel Centralized Teacher with Decentralized Student (CTDS) framework, which consists of a teacher model and a student model. Specifically, the teacher model allocates the team reward by learning individual Q-values conditioned on global observation, while the student model utilizes the partial observations to approximate the Q-values estimated by the teacher model. In this way, CTDS balances the full utilization of global observation during training and the feasibility of decentralized execution for online inference. Our CTDS framework is generic which is ready to be applied upon existing CTDE methods to boost their performance. We conduct experiments on a challenging set of StarCraft II micromanagement tasks to test the effectiveness of our method and the results show that CTDS outperforms the existing value-based MARL methods.