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In recent years, hybrid chaotic image encryption schemes combined with the DNA encryption technology or other technologies have become a research focus of many researchers. However, some researchers neglect security analyses of proposed schemes under the chosen plaintext attack, therefore leaving security vulnerabilities. Considering this situation, we carefully investigate a recently reported hyper-chaotic image encryption scheme using the DNA encryption technology. In this paper, we first point out some issues identified in the reported scheme and make some necessary improvements, and then cryptanalyze it and propose a chosen plaintext attack algorithm. With the proposed attack algorithm, theoretical analyses and test results show that it can completely recover plain images without knowing any secure key related information. Finally, some suggestions for improving the security and practicability of the reported hyper-chaotic image encryption scheme are presented.