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Facial attribute editing has mainly two objectives: 1) translating image from a source domain to a target one, and 2) only changing the facial regions related to a target attribute and preserving the attribute-excluding details. In this work, we propose a Multi-attention U-Net-based Generative Adversarial Network (MU-GAN). First, we replace a classic convolutional encoder-decoder with a symmetric U-Net-like structure in a generator, and then apply an additive attention mechanism to build attention-based U-Net connections for adaptively transferring encoder representations to complement a decoder with attribute-excluding detail and enhance attribute editing ability. Second, a self-attention mechanism is incorporated into convolutional layers for modeling long-range and multi-level dependencies across image regions. experimental results indicate that our method is capable of balancing attribute editing ability and details preservation ability, and can decouple the correlation among attributes. It outperforms the state-of-the-art methods in terms of attribute manipulation accuracy and image quality.