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U-Nets have achieved tremendous success in medical image segmentation. Nevertheless, it may suffer limitations in global (long-range) contextual interactions and edge-detail preservation. In contrast, Transformer has an excellent ability to capture long-range dependencies by leveraging the self-attention mechanism into the encoder. Although Transformer was born to model the long-range dependency on the extracted feature maps, it still suffers from extreme computational and spatial complexities in processing high-resolution 3D feature maps. This motivates us to design the efficiently Transformer-based UNet model and study the feasibility of Transformer-based network architectures for medical image segmentation tasks. To this end, we propose to self-distill a Transformer-based UNet for medical image segmentation, which simultaneously learns global semantic information and local spatial-detailed features. Meanwhile, a local multi-scale fusion block is first proposed to refine fine-grained details from the skipped connections in the encoder by the main CNN stem through self-distillation, only computed during training and removed at inference with minimal overhead. Extensive experiments on BraTS 2019 and CHAOS datasets show that our MISSU achieves the best performance over previous state-of-the-art methods. Code and models are available at \url{https://github.com/wangn123/MISSU.git}