In our urban life, long distance coaches supply a convenient yet economic approach to the transportation of the public. One notable problem is to discover the abnormal stop of the coaches due to the important reason, i.e., illegal pick up on the way which possibly endangers the safety of passengers. It has become a pressing issue to detect the coach abnormal stop with low-quality GPS. In this paper, we propose an unsupervised method that helps transportation managers to efficiently discover the Abnormal Stop Detection (ASD) for long distance coaches. Concretely, our method converts the ASD problem into an unsupervised clustering framework in which both the normal stop and the abnormal one are decomposed. Firstly, we propose a stop duration model for the low frequency GPS based on the assumption that a coach changes speed approximately in a linear approach. Secondly, we strip the abnormal stops from the normal stop points by the low rank assumption. The proposed method is conceptually simple yet efficient, by leveraging low rank assumption to handle normal stop points, our approach enables domain experts to discover the ASD for coaches, from a case study motivated by traffic managers. Datset and code are publicly available at: https://github.com/pangjunbiao/IPPs.