A novel algorithm for detecting corners is presented based on Curvature Scale Space (CSS) and Multi-scale Curvature Product (MSCP). Firstly, the corners of an image are detected at different curvature scale space. Then, a multi-scale curvature polynomial is defined as the sum or multiplication of the curvature of the contour at each scale. The new method can not only enhance curvature extreme peaks effectively, but also suppress noise and prevent smoothing some corners with augment of the scale. In addition, the concavity and convexity of detected corners can be judged by the result sign of the curvature polynomial. Experiment results show that the new method is more effective in corner detection than the other algorithms mentioned in the paper.