We propose an algorithm for extracting singular points of fingerprint image using directional information. First, we extract the candidates of singular points using Poincare index in two(lower and higher) resolutional directional images. Then we remove the false singular points using smoothing technique from lower resolutional directional image. And finally we select the singular points in higher resolution corresponding to those in lower resolution. The possible missing points in lower resolution are found by computing Poincare index algong the proposed small curve. And the reliable points are selected from analysis around them. We also propose a method for segmentation of fingerprint as preprocessing step to enhance the computational speed and the performance of system.