A fiber optic gyroscope signal process dither system permits application of a low amplitude dither signal for many sampling periods without increasing the noise in the sampled outputs due to residual dither signals. A dither loop and an accumulator are added to a closed loop fiber optic gyroscope rotation sensing system. The dither loop has a delay and a gain that are adjusted to match the gain and delay of the fiber gyro loop. A zero mean dither of amplitude sufficient to break up the deadband is injected into to gyro and the dither loop. The dither loop filters the dither signal in the same manner as the gyro loop to provide a signal that is input to a differencing circuit to remove the dither signal from the gyro output.