Wave coupling between the fundamental vetor modal fields of two Identical, polarization maintaining, weakly guiding fibers is analyzed. An improved coupled mode theory is employed, which also applies to anisotropic materials. Coupling coefficients which a the elements of a coupling matrix are calculated and presented as function of the relative tilt angle between the two fiber principal axes. Exact analytical expressions for the eigenvalues and their associated eigenvectors are then given in terms of the elements of this coupling matrix, for any relative tilt angle. Symmetry relations that are found between elements of the coupling matrix much simplify the presentation of the eigenvectors. A weak coupling approximation of the eigenvalue expressions, which is also given, still retains their qualitative proprties.