Problem of recovering the writing order from single-stroked handwritten image can be seen as finding the smoothest Euler path in its graph representation. In this paper, a novel approach is proposed to solve the recovery problem within the framework of the Edge Contiguous Relation (ECR). Firstly, we make local analyses to obtain the possible ECRs at each of the nodes; secondly a global trace is executed to find all of the candidate Euler paths and the smoothest one is selected as a final result. Based on two simple assumptions, we prove a series of theorems to obtain possible ECRs at even node. Double-traced lines are identified by using the weighted matching of general graph. Experiments on the scanned images and offline images converted from the online data of Unipen database have shown that our method achieved 95.2% correct recovery rate.