A lot of techniques have been developed for the encoding of triangular meshes as this is a widely used representation for the description of surface models. Although methods for the encoding of the neighbor information, the connectivity, are near optimal, there is still room for better en-codings of vertex locations, the geometry. Our geometry encoding strategy follows the predictive coding paradigm, which is based on a region growing encoding order. Only the delta vectors between original and predicted locations are encoded in a local coordinate system, which splits into two tangential and one normal component. In this paper we introduce so-called higher order prediction for an improved encoding of the normal component. We first encode the tangential components with parallelogram prediction. Then we fit a higher order surface to the so far encoded geometry. As we encode the normal component as a bending angle, it is found by intersecting the higher order surface with the circle defined by the tangential components. Experimental results show that our strategy allows saving one bit per vertex for the normal component independent of the tangential prediction rule used.