The root-finding problem has a wide range of application in computer-aided design and computer graphics. This study attempts to improve conventional clipping. For a multiple root case

good computational stability is maintained and a higher convergence rate is achieved. This study presents a new clipping method based on space. The proposed method utilizes the good computational stability of Bernstein basis functions

provides a simple method to evaluate the existence of multiple roots

and converts a multiple root case into a simple root case. Compared with conventional cubic clipping methods based on and spaces

the proposed method achieves a better approximation effect. The proposed method can also achieve the convergence rate of 5 for a multiple root case of multiplicity m

which is better than the convergence rates 4/ and 5/ of previous cubic clipping methods. The computational complexity of different cubic clipping methods are close. The new method can evaluate the existence of multiple roots and can achieve a higher convergence rate and a better approximation effect for a multiple root case.