In this paper we confirm the relation between the phase and phase error of the beat signal at the lock-in region of the dither type ring laser gyroscope by numerical calculation. We also study the requirement of the dither noise of an amplitude modulation type for statistical zero averaging of the beat signal phase error, without accumulation. As a result, we find that the dither noise requires the increase and decrease gradients of the dither amplitude, and those gradients should be combined with similar white noise. The slope of the gradient and maximum/minimum amplitude must be changed randomly. We confirm the error accumulation characteristic related to the dither noise by comparison of the two outputs during temperature change, by operating the two kinds dither noise, one is satisfied with the requirement and the other is not.