A frozen-orbital analysis (FZOA) that has been proposed in order to analyze excitation between degenerate orbitals is applied to molecules with I-h symmetry such as (B12H12)(2-) and C-60. In the FZOA approach, the ordering and the energy splittings of the excited states involving degenerate orbitals can be understood through a simple and intuitive picture. FZOA results for molecules with I-h symmetry also reveal that two general rules hold: (i) The highest transition among transitions between degenerate orbitals is dipole-allowed; (ii) The excitation energy of the highest transition is larger than those of the other transitions.