The coherently coupled nonlinear Schrdinger equation of the propagation of a light pulse in a nonlinear birefringence fiber has been utilized.We have studied modulation instability not only in an anomalous dispersion regime but also in a normal dispersion regime when the angle between the polarized direction and the birefringence axes is arbitrary.The results show that the instability polarized region and stability polarized region exist not only in the anomalous dispersion regime but also in the normal dispersion regime. The input pulses have obviously different gain spectra when the instability polarized region and input different power are different.