On-line handwritten character recognition system is a special line of research in image processing and pattern recognition field, it can also considered a special process of in academic researches and production fields in the past decade. The general steps in a recognition system are pre-processing, segmentation, feature extraction and classifications. The techniques of pre-processing stage play an excessive role in the system and directly affect the system performance. The focus of this article is on doing pre-processing stage and providing a most desirable data set form the raw data using in feature extraction and then to increase the rate of recognition system. For this reason, the novel algorithm is presented for finding a critical points set of hand-drawn letters. These critical points help extracting the correct structural and statistical features of on-line character handwriting in any given style writing.