<p>In this study, a new explicit iterative algorithm with a tuning parameter is constructed to solve the Lyapunov matrix equation associated with the discrete-time stochastic systems. Firstly, the boundedness and monotonicity of the proposed algorithm under zero initial condition are studied when the corresponding stochastic system is asymptotical mean-square stable. In addition, some necessary and sufficient conditions are investigated for the convergence of the proposed algorithm. Furthermore, the optimal tuning parameter is studied to achieve the fastest convergence rate of the algorithm for some special cases, and for the general cases, two searching approaches are given to find the optimal tuning parameter. Finally, three numerical examples are taken to illustrate the correctness of the conclusions in this paper.</p>