A novel image encryption algorithm using a combination of 4D discrete hyperchaotic map and DNA encoding is proposed in this work. The used 4D discrete hyperchaotic map has a wider chaotic range, larger Lyapunov exponent, and is more complex than existing hyperchaotic maps. In this work, the generated hyperchaotic sequence is applied to almost every phase of encryption. Here the input image is first converted into binary image sequences and these sequences are globally scrambled by the used 4D discrete hyperchaotic map. To achieve a better encryption performance and to increase the diffusion in the proposed algorithm, DNA algebraic operations (such as DNA addition and subtraction) and complementation are used in the hyperchaotic sequence. The experimental findings demonstrate that the proposed encryption technique is more secure and resistant to common threats than certain other approaches.