Abstract: In this paper,a new solution method for the Lyapunov matrix equation by using U-D factorization method is proposed.The matrix factors Uand D are iterated instead of the iteration of solution matrix P.This new method can improve the accuracy of solution matrix P,while the amount of computation remains the same as the conventional algorithm.The U-D factorization method is also applied to he two step accelerated convergent iterative method"in1.This makes the new method both accurate and fast convergent.