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The problem of constructing a parametric cubic rational curve to interpolate a set of distinct data points is discussed. Unlike the existing methods which includes the determination of knots, the new method constructs parametric curve without the process of determining knots. For each point, a quadratic rational Bezier curve is constructed by the five, four or three convex points. Between each pair of the two adjacent points, a parametric cubic rational curve is constructed by the combination of the two quadratic rational Bezier curves. The constructed cubic rational curve reproduces a conic section exactly if the given data points are taken from the conic section. The comparison of the new method with other ones are included.