As a new technology that combines reversible data hiding and fragile watermarking, image reversible authentication (RA) can not only realize the fragile authentication of images but also recover the original carrier image without distortion while extracting the authentication code. Thus, it is of great significance to authenticate the originality and integrity of images. Existing reversible authentication methods have low authentication accuracy and cannot effectively protect images with complex textures or some areas with complex textures in the images. To this end, this study proposes a new reversible authentication method. Firstly, images to be authenticated are divided into blocks, and the obtained sub-blocks are classified as differential blocks (DB) and shifting blocks (SB) according to their embedding capacity. Different reversible embedding methods are employed to embed the authentication codes into different types of blocks. It also adopts a hierarchical embedding strategy to increase embedding capacity and improve the authentication effects of each sub-block. On the authentication side, tamper detection and localization can be realized by the authentication code extracted from each sub-block. In addition, this method can be combined with dilation and corrosion in morphology to refine tamper detection marks and further improve the detection accuracy rate. Experimental results show that the proposed method can protect images with smooth texture and complex texture under the same authentication accuracy, and can also realize independent authentication and restoration of almost all sub-blocks, which has widespread applicability.