Square-wave frequency modulation is widely used in resonator micro-optic gyro(RMOG).The triangle phase modulation waveform for the realization of square-wave frequency modulation eliminates the output fluctuation induced by the reset time and reset error in sawtooth modulation waveform.The influence on the output intensity by the turning points of triangle phase modulation waveform is analyzed.Moreover,outputs under modulation waveforms with different frequency bases and different rotation rates are theoretically calculated.Furthermore,the pectinate filter is involved to avoid the output error induced by the discontinuous frequency-modulation.Finally,the influence of the discontinuous frequency-modulation is observed in ROMG experimental setup,and the pectinate filter greatly improves the gyro bias stability from 1.96 °/s to 0.11 °/s.