In this paper we confirm the disappearance of dynamic lock-in simply by increasing the dither noise magnitude of the ring laser gyroscope by numerical and experimental method. After that, we numerically study the relation between the dither noise forms and scale factor non-linearities by comparing those of the two case outputs which are individually generated by operating with the two types of dither noise forms. The first one is the simple form composed of consecutive alternations of the random increasing and decreasing parts but maximum and minimum dither envelopes are scarcely changeable. And the second one is similar to the first one but maximum and minimum dither envelopes are randomly changable. As a result, we find that the scale factor non-linearity could be improved by the second one. And we confirm those results by experimental measurements.