Neural network algorithms on MCA (minor component analysis) are of importance in signal processing. Coupled algorithm can mitigate the speed-stability problem which exists in most non-coupled algorithms. Although some coupled algorithms have been proposed so far, there exists complex computation in them. In this paper, based on a novel information criterion and by modifying the Newton's method, we propose one algorithm which is coupled. In the derivation of our algorithms, it is more accurate and faster to obtain the results compared with traditional methods, because it is not needed to calculate the inverse Hessian matrix. The experimental results show that the proposed algorithm has higher accuracy, faster convergence and better robust performance than the existing coupling algorithm.