Fingerprint matching algorithm is a key step in fingerprint recognition system. Though there are many existing matching algorithms, there has been inability to match fingerprints in linear time. In this paper we present a novel biometric approach to match fingerprints that run in linear time. We match the minutiae in the fingerprint by constructing a nearest neighbor vector (NNV) considering its k-nearest neighbors. The consolidation of these matched minutiae points is done by incorporating them in binary tree that propagates simultaneously in both fingerprints. This helps our algorithm to run in O(n) time in contrast to many existing algorithms when reference core point is available. We analyze the resulting improvement in computational complexity and present experimental evaluation over FVC2002 database