Most fingerprint recognition systems are based on matching the location and orientation attributes of minutia points. In this paper, we propose a localized minutiae phase spectrum representation that encodes the local minutiae structure in the neighborhood of a given minutia point as a fixed-length binary code. Since this representation is invariant to global transformations (e.g., translation and rotation), the correspondences between the minutia points from two different fingerprints can be easily established based on the similarity (Hamming distance) between their phase spectral codes. In addition to determining the local minutiae similarities, a global similarity score can also be computed by aligning the query to the template based on the estimated correspondences and finding the similarity between the global phase spectra of the aligned minutiae sets. While the local similarity scores are robust to nonlinear fingerprint distortion, the global similarity score captures the highly distinctive spatial relationships between all the minutia points. Therefore, a combination of these two similarity measures provides high recognition accuracy. Experiments on the public-domain FVC2002 databases (DB1 and DB2) and FVC2006-DB2 demonstrate that the proposed approach achieves less than 1% Equal Error Rate, which is better than the state-of-the-art fingerprint matchers using only the location and orientation of minutia points.