One of the universally studied research topics is a reversible data hiding approach because of its wide applications in medical image transmission, cloud computing as well as in military services. In the introduced scheme stated in this paper, a new RDH scheme in encrypted images is proposed which ensures a good embedding rate without compromising the bit error rate. The scheme introduced in this manuscript uses a new measure that is computationally efficient and ensures real-time performance. In the proposed scheme, the original image is divided into blocks and in each block, one secret message bit is hidden by the data hider. All the pixels in the image block are categorized into two classes: black pixels and white pixels based on the predefined checkerboard pattern. The data hiding is performed by mapping the pixel values in the white position to a new value, only if the data hider wants to hide a secret bit 1. At the time of data extraction and image recovery, the closeness between the adjacent pixels is analyzed by considering a pair of adjacent black pixels and white pixels from the quantized image blocks. The overall experimental study of the proposed scheme is carried out using the standard images from the USC-SIPI image dataset managed by the University of Southern California.