The personal identification procedure through the fingerprints is divided as the classification process by the type of the fingerprints and the matching process to confirm oneself. Many existing researches for the classification and the matching of the fingerprint depend on the number of the minutiae of the fingerprints and the flow patterns by their direction information. In this paper, we focus on extracting the singular points by using the flow patterns of the direction information from identification. The extracted singular points are utilized as a standard point for the matching process by connecting with the extracted information from the singular point embodied. The orthogonal coordinates which is generated by the axises of the standard point can increase the accuracy of the fingerprints matching because of minimizing the effects on the location changes of the fingerprint images.