This paper presents a new 2D polygon clipping method, based on an extension to the Sutherland-Cohen 2D line clipping method. After discussing three basic polygon clipping algorithms, a different approach is proposed, explaining the principles of a new algorithm and presenting it step by step. An example implementation of the algorithm is given along with some results. A comparison between the proposed method, the Liang and Barsky algorithm, and the Sutherland-Hodgman algorithm is also given, showing performances up to eight times the speed of the Sutherland-Hodgman algorithm, and up to three times the Liang and Barsky algorithm. The algorithm proposed here can use floating point or integer operations; this can be useful for fast or simple implementations.