This paper presents a robust minutiae based method for fingerprint verification. The proposed method uses Delaunay Triangulation to represent minutiae as nodes of a connected graph composed of triangles. The minimum angle over all triangulations is maximized, which gives local stability to the constructed structures against rotation and translation variations. Geometric thresholds and minutiae data were used to characterize the triangulations created from input and template fingerprint images. The effectiveness of the proposed method is confirmed through calculations of false acceptance rate (FAR), false rejected rate (FRR) and equal error rate (EER) over FVC2002 databases compared to the results of other approaches.