The singular points of fingerprints, viz. core and delta, are important referential points for the classification of fingerprints. Several conventional approaches such as the Poincare index method have been proposed; however, these approaches are not reliable with poor-quality fingerprints. This paper proposes a new core and delta detection employing singular candidate analysis and an extended relational graph. Singular candidate analysis allows the use both the local and global features of ridge direction patterns and realizes high tolerance to local image noise; this involves the extraction of locations where there is high probability of the existence of a singular point. Experimental results using the fingerprint image databases FVC2000 and FVC2002, which include several poor-quality images, show that the success rate of the proposed approach is 10% higher than that of the Poincare index method for singularity detection, although the average computation time is 15%-30% greater.