Abstract: In CAGD, the Said-Ball representation for a polynomial curve has two advantages over the Bezier representation, since the degrees of Said-Ball basis are distributed in a step type. One advantage is that the recursive algorithm of Said-Ball curve for evaluating a polynomial curve runs twice as fast as the de Casteljau algorithm of Bezier curve. Another is that the operations of degree elevation and reduction for a polynomial curve in Said-Ball form are simpler and faster than in Bezier form. Interval Said-Ball curves are new representation forms of parametric curves that can embody a complete description of coefficient errors. Using this new representation, the problem of lack of robustness in all state-of-the art CAD systems can be largely overcome. In this paper this concept has been discussed to form a new curve over rectangular domain such that its parameter varies in an arbitrary range [a,b] instead of standard parameter [0,1], where a and b are real and, we also want that curve gets generated within the given error tolerance limit. The four fixed Kharitonov's polynomials (four fixed SB curves) associated with the original interval SB curve are obtained. A new parameterization is applied to the four fixed Kharitonov's polynomials (four fixed SB curves) using matrix representation. Finally, the required interval control points are obtained from the reparametrized fixed control points of the four fixed SB curves. A numerical example is included in order to demonstrate the effectiveness of the proposed method.