Fragile watermarking has attracted a lot of attention in the last decade. An interesting approach, presented in 2011 by Lin et al., results in very high quality of the watermarked images. However, after a thorough examination of the paper, a few improvements are proposed in our revised version of the algorithm in order to overcome some shortcomings. In particular, changes to the pseudocode and modifications to deal with pixel saturation are suggested, along with a way to improve the scheme security. Finally, a deeper analysis of the security is presented.