Based on the coupled-mode theory, a simple method to distinguish circular-birefringence fibers is presented. It is indicated that in a linear-birefringence single-mode fiber the coupling coefficient between two orthogonnal linearly polarized modes is a imaginary number, and the coupling coefficient will be real while in a circular-birefringence fiber. From this fact and the symmatry of the refractive index profile of the fiber cross-sections, we conclude that fiber structure is kept unchanged in case of opposite location of fiber axes is one of the three necessary conditions for a circular birefringent fiber. According to this rule, only twisted fibers and helical fibers (drawn in viscous state at a high temperature) are really circular birefringent fibers.