The finite-element model of the geopotential and its gradient as introduced by Junkins, is significantly improved by the use of orthonormal polynomials. The computational effort to obtain the modeling constants via the normal equations is greatly reduced, especially if the order of approximation is increased. Moreover, replacing an existing gravity representation (such as a spherical harmonic series), can now be more rigorously approached; it is possible (for example) to determine the coefficients of the local approximations by analytical integration. We include several illustrative examples.