A constructive approach is adopted to build B-spline like basis for a rational cubic spline curve with certain number of parameters to produce some shape control in the area of computer graphics. This method provides not only a large variety of very interesting shape controls like biased. point and interval tensions but, as a special case, also recovers the cubic B-spline curve and the rational cubic spline with tension [Gregory and Sarfraz'90]. This method is also a C2 alternative to the GC2 or C1 spline methods like √-spline of Nielson [Nielson 74]. β-splines [Barsky'81]. γ-splines of Boehrn [Boehm.85] and weighted splines [Foley'87]. The method for evaluating this rational cubic B-spline curve is suggested by a transformation to Bernstem-Bezier form.