Abstract: A new detection algorithm of fingerprint singular points is proposed in this paper, based on flow field and Laurent series. Fingerprint orientation flow field is obtained, by using the gradient of fingerprint scalar field. Candidate singularities are detected using the cross-correlation energy calculated between fingerprint orientation flow field and complex-valued filters derived from a novel multi-scale Laurent polynomial model, which allows for rotation invariant detection of singular points in general flow fields. The algorithm is tested on SPD2010 database. Results show that the proposed algorithm outperforms the best detecting algorithm by large margin and the detection is invariant to rotational transformations.