Symmetry detection is important in the area of computer vision. A simple and fast algorithm for the recovery of rotational symmetry parameters is developed. The fold number of a rotationally symmetrical shape is obtained from the gradient orientation histogram of the input gray-level image using the Fourier method, based on the relationship between the periodicity of the orientation histogram and the fold number of the symmetrical shape. It takes only 0.06 s CPU time for a 256 3256 gray image on a Sun SPARC10. Both simulated and real images are tested and the results are very convincing.