This paper is an improved version of Zhang's reversibility improved data hiding method in encrypted images. The original work randomly selects p%(0 < p ≤ 20) pixels from an original image to obtain the estimation error for secret data embedding. In this work, we estimate half of the pixels in the original image to obtain the estimation error so that the maximum embedding rate can be significantly improved while keeping a high image quality of the marked decrypted image. The experimental results show that our proposed method has a higher performance than Zhang's method.