The paper proposes an original prediction error expansion (PEE) reversible watermarking scheme that exploits the sign of the prediction error in order to prevent the overflow/underflow of the pixels close to the bounds of the graylevel range. More precisely, the pixels close to black are directly embedded by PEE when the prediction error is positive. Similarly, the ones close to white are embedded in case of negative errors. When the prediction error sign does not allow error expansion, an original solution is proposed. The pixel is left unchanged and one of its upper diagonal neighbors is embedded by PEE, but with a different prediction error. The diagonal neighbor is selected in order to prevent overflow/underflow. The proposed prediction error strategy ensures detection and reversibility without any additional information. The scheme is of interest for images with large areas of black and white pixels as, for instance, medical images.