The adjoint transformation of electromagnetic fields for uniform isotropic dielectric is considered for guided waves in an optical fiber. The necessary and sufficient condition for two solutions to be a pair of partners is derived. The modes of guided waves are analyzed under this condition. It is proved that the dispersive normal modes do not exist in the case of non-axial symmetry. The guided modes in such cases are modes of critical refraction, which has a discrete spectrum. The dispersive normal modes exist in axial symmetrical cases. Theoretical predictions are comparable with the experiment data. The behaviour of the fundamental mode shows that it is a mode of critical refraction rather than a dispersive normal mode as is predicted by the theory.