Abstract: The classical four-point interpolating subdivision scheme is a special case of this kind of subdivision.The sufficient conditions of the uniform convergence property and C^k continuity properties of the four-point binary subdivision scheme with two parameters are proved.It can generate C⁴ limit functions.Using the presented scheme one can not only model smooth interpolating subdivision curves but also can model approximating subdivision curves with high smoothness.One can modify and control the shape of the smooth subdivision curves by choosing these two parameters appropriately.The convexity preserving property is examined when it is applied to uniform convex data.Conditions on the two shape parameters guaranteeing preservation of convexity are derived.