Fingerprint has remained a very vital index for human recognition. In the field of security, series of Automatic Fingerprint Identification Systems (AFIS) have been developed. One of the indices for evaluating the contributions of these systems to the enforcement of security is the degree with which they appropriately verify or identify input fingerprints. This degree is generally determined by the quality of the fingerprint images and the efficiency of the algorithm. In this paper, some of the sub-models of an existing mathematical algorithm for the fingerprint image enhancement were modified to obtain new and improved versions. The new versions consist of different mathematical models for fingerprint image segmentation, normalization, ridge orientation estimation, ridge frequency estimation, Gabor filtering, binarization and thinning. The implementation was carried out in an environment characterized by Window Vista Home Basic operating system as platform and Matrix Laboratory (MatLab) as frontend engine. Synthetic images as well as real fingerprints obtained from the FVC2004 fingerprint database DB3 set A were used to test the adequacy of the modified sub-models and the resulting algorithm. The results show that the modified sub-models perform well with significant improvement over the original versions. The results also show the necessity of each level of the enhancement.