Designing a powerful fragile watermarking technique for authenticating three-dimensional (3-D) polygonal meshes is a very difficult task. Yeo and Yeung  were first to propose a fragile watermarking method to perform authentication of 3-D polygonal meshes. Although their method can authenticate the integrity of 3-D polygonal meshes, it cannot be used for localization of changes. In addition, it is unable to distinguish malicious attacks from incidental data processings. In this paper, we trade off the causality problem in Yeo and Yeung's method for a new fragile watermarking scheme. The proposed scheme can not only achieve localization of malicious modifications in visual inspection, but also is immune to certain incidental data processings (such as quantization of vertex coordinates and vertex reordering). During the process of watermark embedding, a local mesh parameterization approach is employed to perturb the coordinates of invalid vertices while cautiously maintaining the visual appearance of the original model. Since the proposed embedding method is independent of the order of vertices, the hidden watermark is immune to some attacks, such as vertex reordering. In addition, the proposed method can be used to perform region-based tampering detection. The experimental results have shown that the proposed fragile watermarking scheme is indeed powerful.