This document describes a new methodology for improving the accuracy of fingerprint verification systems. It proposes detecting singular points like core and delta points, and indexing templates based on the occurrence of delta points relative to the core point. Experiments on the FVC2006 database show the proposed method achieves higher recognition rates and lower false acceptance and rejection rates compared to existing minutiae-based matching techniques, especially for distorted images. It provides a concise way to represent templates and allows for faster matching by first comparing singular point information before minutiae points.