In this article, a new reversible data hiding method using most significant bits and center shifting technique in dual images is proposed. The proposed reversible data hiding method aims to securely hide high-capacity secret data. Instead of directly embedding the secret data, the method calculates new values with (n + 1) bits secret data and the n most significant bits of the cover image pixel values. Thus, it is impossible to extract secret data without obtaining the original cover image. Also, the center shifting process is performed to minimize the mean square error. After this process, the secret data to be hidden in the dual images are in the range [−3×2(n−1)+1, 3×2(n−1)−1]. The pixel values of stego images are obtained by using the secret data in this range value and cover image pixel values. As a result of experimental studies, when the payload is 2.5 bits per pixel (bpp), the peak signal-to-noise ratio value (PSNR), which expresses the visual quality, is above 34 (dB). In addition, the proposed method has proven secure against RS (regular and singular) analysis attacks.