A biometric identification system must answer the question: who is the person? It must recognize the individual with no other data than the digital representation of their biometric trait. Indexing significantly reduces the number of candidates to verify, however they depend entirely on the quality of the index and the features extracted from the fingerprint. This article presents a robust indexing scheme against rotations, translations and elastic deformations in the skin, based on Delaunay triangulation, maintaining acceptable response times and having a better penetration rate than the published works consulted. To determine these characteristics, a topological structure based on Delaunay triangulation will be associated, where the coordinates of the vertices of the generated triangles correspond to those of the minutiae extracted from the fingerprint.