Fingerprint recognition is a well-studied research area in which significant results have been achieved. Fingerprint recognition can be divided into two tasks: verification and identification. Fingerprint verification is used to verify the identity of an individual by 1:1 matching whereas identification is used to establish the identity by 1:N matching. Fingerprint identification thus becomes more challenging than verification because of high system penetration and false acceptance rate. In the resolution of this problem, indexing algorithms have a fundamental role. In the literature, there are several proposals that make use of different features to characterize fingerprints. Fingerprint indexing is an efficient technique that greatly improves the performance of fingerprint based person authentication systems by reducing the number of comparisons. This article presents a novel fingerprint indexing algorithm for large databases. A spherical locality-sensitive hashing scheme has been designed relying on generalized Chebyshev polynomials approximation model. One general approach to LSH is to "hash" items several times, in such a way that similar items are more likely to be hashed to the same bucket than dissimilar items. One can consider any pair that hashed to the same bucket for any of the hashings to be a candidate pair. The analysis and the experimental results show a good performance in terms of accuracy and computational complexity. Indexing experiments show remarkable results using public fingerprint database FVC2004 DB1.