With the development of cloud computing, data privacy has become a major problem. Reversible data hiding in encrypted images (RDHEI) is an effective technique to embed data in the encrypted domain. Indeed, a lot of methods have been proposed, but none allows a large amount of embedding capacity with a perfect reversibility. In this work, we present a new method of reversible data hiding in encrypted images using MSB (most significant bit) prediction. In order to reconstruct the original image without any errors during the decryption phase, we adapt the to-be-inserted message. Some of the pixels' MSB values are used to highlight the prediction errors and the remaining values are replaced by bits of the secret message. Results show that it is still possible to embed a large message (payload close to 1 bpp).