A singular point or singularity on fingerprint is considered as a fingerprint landmark due its scale, shift, and rotation immutability. It is used for both fingerprint classification and alignment in automatic fingerprint identification systems. This paper presents a comparative study between two singular point detection methods available in the literature. The Poincaré index method is the most popular approach, and the complex filter is another proposed method applied on the complex directional images. The maximum complex filter response is highly related to the regions with abrupt changes in the ridge orientations. These regions have a high probability to contain a singular point. The optimum detection method in both processing time and detection accuracy will be updated to suite our efficient classification method. The experimental evaluation for both methods proves that the accuracy achieved by complex filter is up to 95% with considerable processing time compared to 90% with Poincaré index method.