Zernike moments have been one of the most commonly used feature vectors for recognizing rotated patterns due to its rotation invariant characteristics. In order to reduce its expensive computational cost, several methods have been proposed to lower the complexity. One of the methods proposed by mukundan and K. R. Ramakrishnan[1], however, is not rotation invariant. In this paper, we propose another method that not only reduces the computational cost but preserves the rotation invariant characteristics. In the experiment, we compare our method with others, in terms of computing time and the accuracy of moment feature at different rotational angle of an object in image.