The independent right censorship (RC) model assumes that the survival time and censoring time are independent. Williams and Lagakos (W&L) (1977) propose a continuous dependent RC model. They show that it is equivalent to a continuous independent RC model. Yu et al.} (2012) study another dependent RC model, say Model 2, without the continuity restriction, which is essentially the necessary and sufficient condition for the product-limit-estimator (PLE) being consistent for all time within the largest exact observation under the non-parametric set-up. However the asymptotic normality of the PLE under that model is not addressed due to technical difficulties. In this paper, we show that (1) the continuous (but not the discrete) W&L model is a special case of Model 2; (2) Model 2 is equivalent to an independent RC model, extending W&L's result. Thus the asymptotic normality of the PLE under Model 2 follows from the existing results in the literature under the independent RC model.