Abstract: It is very important to extract singular points accurately and reliably for classification and matching of fingerprints. To deal with the difficulty in extracting singular points from fingerprint image of low quality, a two-phase algorithm for singular points extraction is presented in this paper. In the first phase, to heighten anti-noise capability of traditional Poincare index and reduce false singularities, an improved algorithm for Poincare index is proposed, and then it is used to extract candidate singularities. In the second phase, based on the characteristic that Gaussian-Hermite moment attribution between singular region and ordinary region is different, it is along the direction orthogonal local ridge orientation in ordinary area while along all the directions in singular region. Gaussian-Hermite moment attribution for each candidate in its round neighborhood is calculated to determine whether it is true singularity or not. Because this two-phase method effectively assembles information of ridge orientation and coherence in singularitys neighborhood，it can extract singularities in a comparatively accurate and reliable way. Experimental results show its effectiveness and robusticity. 500 fingerprint images from the NIST-4 database are used for an experimental test, and the accuracy rate on identifying singular points is 93.05% （96.93% for core points and 86.43% for delta points）.