In cooperative multi-agent reinforcement learning (MARL), the environmental stochasticity and uncertainties will increase exponentially when the number of agents increases, which puts hard pressure on how to come up with a compact latent representation from partial observation for boosting value decomposition. To tackle these issues, we propose a simple yet powerful method that alleviates partial observability and efficiently promotes coordination by introducing the UNit-wise attentive State Representation (UNSR). In UNSR, each agent learns a compact and disentangled unit-wise state representation outputted from transformer blocks, and produces its local action-value function. The proposed UNSR is used to boost the value decomposition with a multi-head attention mechanism for producing efficient credit assignment in the mixing network, providing an efficient reasoning path between the individual value function and joint value function. Experimental results demonstrate that our method achieves superior performance and data efficiency compared to solid baselines on the StarCraft II micromanagement challenge. Additional ablation experiments also help identify the key factors contributing to the performance of UNSR.