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In this paper, we propose a novel hue-correction scheme for color-image-enhancement algorithms including deep-learning-based ones. Although hue-correction schemes for color-image enhancement have already been proposed, there are no schemes that can both perfectly remove perceptual hue-distortion on the basis of CIEDE2000 and be applicable to any image-enhancement algorithms. In contrast, the proposed scheme can perfectly remove hue distortion caused by any image-enhancement algorithm such as deep-learning-based ones on the basis of CIEDE2000. Furthermore, the use of a gamut-mapping method in the proposed scheme enables us to compress a color gamut into an output RGB color gamut, without hue changes. Experimental results show that the proposed scheme can completely correct hue distortion caused by image-enhancement algorithms while maintaining the performance of the algorithms and ensuring the color gamut of output images.