In the Freezing Rotation illusion a stimulus rotating with a constant velocity is perceived as stationary on the screen, when it is presented in front of a background pattern that moves with a sinusoidal velocity profile, during the phase in which stimulus and background rotate in the same direction. It has been suggested that this illusion is caused by the interfering effect of induced motion resulting from the relative motion between the centre and the surround. Since the magnitude of such an induced motion component presumably relates to the difference between background and centre velocities, the illusion itself should also be related to the amount of relative motion between the centre and the surround, and it should not occur when this difference is zero. We present evidence here that this hypothesis is incorrect. First, we show that the illusion also occurs when the background moves with a constant velocity instead of sinusoidally. Second, we show that the illusion consists of a fixed underestimation of centre velocity when the centre and the surround move in the same direction and a fixed overestimation of centre velocity when they move in opposite directions or when the background remains stationary. The amount of underestimation and overestimation of velocity is not related to the velocity difference between the centre and the surround. Some factors that may be relevant to the explanation of the illusion are discussed.