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Reversible data hiding (RDH) is a special class of steganography, in which the cover image can be perfectly recovered upon the extraction of the secret data. However, most image-based RDH schemes focus on improving capacity–distortion performance. In this paper, we propose a novel RDH scheme which not only effectively conceals the traces left by HS but also improves capacity–distortion performance. First, high-precision edge predictor LS-ET (Least Square predictor with Edge Type) is proposed, and the predictor divides pixels into five types, i.e., weak edge, horizontal edge, vertical edge, positive diagonal edge, and negative diagonal edge. Different types of target pixels utilize different training pixels with stronger local consistency to improve accuracy. Then, a novel prediction-based histogram-shifting (HS) framework is designed to conceal embedding traces in the stego images. Finally, we improve both the data-coding method and the skipping embedding strategy to improve the image quality. Experimental results demonstrate that the capacity–distortion performance of the proposed scheme outperforms the other trace concealment schemes and is comparable to the state-of-the-art schemes utilizing sorting technique, multiple histogram modification, and excellent LS-based predictors. Moreover, it can conceal the embedding traces left by the traditional HS schemes to a certain extent, reducing the risk of being steganalyzed.