Problem of recovering a writing order from singlestroked 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 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. The two main contributions are: 1) Based on two simple assumptions, we prove a series of theorems to obtain possible ECRs at even node. 2) We introduce a method to identify doubletraced lines by using 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.