Reversible Data Hiding (RDH) is a practical and efficient technique for information encryption. Among its methods, the Pixel-Value Ordering (PVO) algorithm and its variants primarily modify prediction errors to embed information. However, both the classic PVO and its improved versions, such as IPVO and PVO-k, share a common limitation: their maximum data embedding capacity for a given grayscale image is relatively low. This poses a challenge when large amounts of data need to be embedded into an image. In response to these issues, this paper proposes an improved design targeting the PVO-k algorithm. We have reconstructed the mapping scheme of the PVO-k algorithm to maximize the number of pixels that can embed encrypted information. Experimental validations show that our proposed scheme significantly surpasses previous algorithms in terms of the maximum data embedding capacity. For instance, when embedding information into a grayscale image of an airplane, our method's capacity exceeds that of PVO-k by 11,207 bits, PVO by 8,004 bits, and IPVO by 4,562 bits. The results demonstrate that our algorithm holds substantial advantages over existing methods and introduces innovative mapping ideas, laying a foundation for future research in reversible data hiding in images.