A set of Zernike moments has been successfully used for object recognition or content-based image retrieval systems. Real time applications using Zernike moments, however, have been limited due to its complicated definition. Conventional methods to compute Zernike moments fast have focused mainly on the radial components of the moments. In this paper, utilizing symmetric/anti-symmetric properties of Zernike basis functions, we propose a fast and efficient method for Zernike moments. By reducing the number of operations to one quarter of the conventional methods in the proposed method, the computation time to generate Zernike basis functions was reduced to about 20% compared with conventional methods. In addition, the amount of memory required for efficient computation of the moments is also reduced to a quarter. We also showed that the algorithm can be extended to compute the similar classes of rotational moments, such as pseudo-Zernike moments, and ART descriptors in same manner.