A recent study by Fok et al. (Oxf Bull Econ Stat 77:872-896,2015) concludes that there is a low-pay no-pay cycle for males and females in the Australian labour market. This note re-estimates the model of that study using the same data. It is found that Fok et al. (2015) conclusion is based on a model specification that assumes zero correlation of unobserved heterogeneity between the different labour force states modelled. The results of this note show that when the zero correlation restriction is relaxed, there is no evidence of a low-pay no-pay cycle for either males or females. It is also found that the marginal effect estimates used in Fok et al. (2015) to draw the low-pay no-pay cycle conclusion for males and females have been estimated imprecisely. Furthermore, contrary to what Fok et al. (2015) have concluded, the results of this note show that there is no evidence on heterogeneity in the low-pay no-pay cycle across the demographic subgroups examined by Fok et al. (2015).