Bhardwaj[11] has recently proposed a method for reversible data hiding in a cover image, which has a very high data hiding capacity. This technique sometimes does not work properly. Singh-Singh[12] has overcome its limitation, which also has very good data hiding capacity. We find that the Singh-Singh’s method does not hide the confidential data in all pixels. We improve the Singh-Singh’s method so that it can hide the secret data in all image pixels if required. Our proposed method can hide 2.49 bits of confidential data in a byte, whereas the Singh-Singh’s method can hide 2.24 bits of confidential data in a byte.