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Strong modes competition makes only one of o-light and e-light oscillate in a birefringent dual-frequency laser when the angle between the crystalline axis and the laser beam is nearly zero. When the oscillated mode is in a different part of the gain curve, the detected intensity curves of o-light and e-light are quite different in the existence of optical feedback. The curves are divided into five cases. Three cases of the experimental results can be used for direction discrimination. The polarization characteristics of the birefringent cavity He-Ne laser are also discussed without optical feedback.