Domain decomposition parallel algorithms for one-and two-dimensional diffusion equations are studied by using multi-step evaluation revisions for interface points with fractional temporal index.Stability conditions are loose.In the algorithm,schemes with fractional step and large spacing discretization are used to evaluate interface points.The algorithms have same accuracy as full implicit method,while their stability bounds are released by q,the number of fractional step evaluations on interfaces between two neighboring temporal steps,times compared with existing algorithms.Convergence is proven rigorously with discrete maximum principle.Numerical experiments on parallel computers confirnl theoretical conclusions.They demonstrate looser stability conditions,good accuracy and parallel expansibility of the algorithms.