An Er-doped bidirectional ring fiber laser with 90 degrees Faraday rotator in the resonator is investigated both theoretically and experimentally, Two different single-longitudinal-mode bidirectional behaviors are demonstrated, Namely, generation of the orto-conjugated counterpropagating modes pairs and generation of the complex-conjugated counterpropagating modes pairs are obtained separately. Considerable stabilization of the nonreciprocal frequency bias produced by the Faraday rotator is achieved in the latter case.