Pixel-value-ordering (PVO) appears as an efficient solution for high-fidelity reversible data hiding. State-of-the-art PVO schemes split the host image into blocks, sort pixels within the blocks based on their graylevel and, finally, embed data into some differences between the sorted values. This paper investigates the use of the prediction error instead of the pixel graylevel both for ordering and embedding. The proposed prediction-error-ordering (PEO) scheme also introduces a two-stage procedure by splitting each block in two sets following a chessboard pattern and by processing set by set each block. The pixels of one set are used to classify and predict the ones of the other set and vice-versa. The proposed PEO approach outperforms the state-of-the-art PVO schemes.