A new technique is proposed for determining the refractive index and thickness of anisotropic films. Suppose the film is aligned in the X-Y plane, and that the plane of incidence includes the X-axis. From the reflectances of S- and P- polarized light, the principal refractive indices nx, ny, and nz can be obtained along with the film thickness d. First, ny and d can be derived from the S-polarized reflectance, since the S-polarization is parallel to the Y- axis. It is also possible to derive nx in the same way. The P-polarization is in the X-Z plane and Fresnel equations for P-polarization are expressed by nx, nz, and d. Therefore, nz can be determined using the P-polarized reflectance and the values already calculated for nx and d. Trial measurements are made on a Sol-Gel derived LiNbO3 film on an Al2O3 substrate, using a system with a reflectance measurement accuracy of the order of 0.01%. The values obtained for ny (equals nx), nz and d are 1.980, 2.056, and 107.5 nm, respectively. According to the results of this simulation, the accuracy of the obtained values can be estimated as < 0.3%.