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We propose an end-to-end unpaired learning approach to screen-shot image demoiréing based on cyclic moiré learning. The proposed cyclic moiré learning algorithm consists of the moiréing network and the demoiréing network. The moiréing network generates moiré images to construct a pseudo-paired set of moiré and clean images. Then, the demoiréing network is trained in a supervised manner using the generated pseudo-paired dataset to remove moiré artifacts. In the moiréing network, the moiré generation is separately learned as global pixel intensity degradation and moiré pattern generation for more realistic moiré artifact generation. Furthermore, the moiréing network and the demoiréing network are integrated together to be trained in an end-to-end manner. Experimental results on different datasets demonstrate that the proposed algorithm significantly outperforms state-of-the-art unsupervised demoiréing algorithms as well as image restoration algorithms.