For reversible data hiding in encrypted images (RDHEI), the private information in the original image content is protected and the embedded secret data can be used to manage the encrypted image. Up to now, many RDHEI algorithms have been reported, however, these reported RDHEI algorithms cannot achieve a high embedding capacity. Therefore, this article proposes a new RDHEI scheme, which will have improved performance. The main contributions of the proposed scheme include two points: chunk encryption (CE) and redundancy matrix representation (RMR). First, different from the encryption method of pixel-by-pixel encryption used in the previous RDHEI algorithms, CE is the method that uses the traditional exclusive-or (XOR) method to encrypt the original image in chunks. By using the CE method, redundancy will be retained in the encrypted chunks. Second, the RMR method is designed to generate available room for accommodating secret data in redundancy matrices, which are existed in some encrypted chunks. Experimental results show that the proposed scheme achieves a high embedding capacity and the directly decrypted images retain high quality.