Abstract: The Euler number is one of the most important topological properties in a binary image. Aiming at the problem on repeated checking of pixels in the conventional computing algorithms, a new algorithm was proposed for computing the Euler number based on counting bit-quads in the given image. In the proposed algorithm, four states are constructed and taking advantage of transitions among the states, pixels can be avoided to check repeatedly. Furthermore, fewer bit-quad patterns were used in the proposed algorithm in order to improve the efficiency of the algorithm. Experimental results on various kinds of images demonstrated that the proposed algorithm is more efficient than conventional Euler number computing algorithms in most cases.