In present paper,this scheme is used to a parabolic singularly perturbed problem.After some subtle analysis,a uniformly in ε convergent order h|ln h|~(1/2)+τ is achieved (h is the space step and τ is the time step),which sharpens the results in present literature.Furthermore,it implies that the accuracy order in M.Stynes's paper(1991) is actuallay h|ln h|~(1/2) rather than h~(1/2).