This article continues the investigation started in Lipovetsky and Dyn (2016) on subdivision schemes refining 2D point-normal pairs, obtained by modifying linear subdivision schemes using the circle average. While in Lipovetsky and Dyn (2016) the convergence of the Modified Lane–Riesenfeld algorithm and the Modified 4-Point schemes is proved, here we show that the curves generated by these two schemes are C 1. • Further investigations of subdivision schemes refining point-normal pairs based on the circle average. • Deriving more properties of the circle average. • Showing C 1 smoothness of two modified schemes with the circle average. • Conjecturing C 1 smoothness for a wider class of modified subdivision schemes.