Fingerprints have long been used in automated fingerprint identification or verification systems. Singular points (SPs), namely the core and delta point, are the basic features widely used for fingerprint registration, orientation field estimation, and fingerprint classification. In this study, we propose an adaptive method to detect SPs in a fingerprint image. The algorithm consists of three stages. First, an innovative enhancement method based on singular value decomposition is applied to remove the background of the fingerprint image. Second, a blurring detection and boundary segmentation algorithm based on the innovative image enhancement is proposed to detect the region of impression. Finally, an adaptive method based on wavelet extrema and the Henry system for core point detection is proposed. Experiments conducted using the FVC2002 DB1 and DB2 databases prove that our method can detect SPs reliably.