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In this paper, we develop a novel transformer-based generative adversarial neural network called U-Transformer for generalised image outpainting problem. Different from most present image outpainting methods conducting horizontal extrapolation, our generalised image outpainting could extrapolate visual context all-side around a given image with plausible structure and details even for complicated scenery, building, and art images. Specifically, we design a generator as an encoder-to-decoder structure embedded with the popular Swin Transformer blocks. As such, our novel neural network can better cope with image long-range dependencies which are crucially important for generalised image outpainting. We propose additionally a U-shaped structure and multi-view Temporal Spatial Predictor (TSP) module to reinforce image self-reconstruction as well as unknown-part prediction smoothly and realistically. By adjusting the predicting step in the TSP module in the testing stage, we can generate arbitrary outpainting size given the input sub-image. We experimentally demonstrate that our proposed method could produce visually appealing results for generalized image outpainting against the state-of-the-art image outpainting approaches.