Delaunay triangulation is suitable for fingerprint matching because of its robustness to rotation and translation. However, missing and spurious minutiae degrade the performance and computational efficiency. In this paper, we propose a method of combining local quality assessment and 4-category minutiae classification to improve accuracy and decrease computational complexity in matching process. Experimental results suggest that removing low quality areas from matching candidate areas and classifying minutiae improve computational efficiency without degrading performance. The results proved that the proposed algorithm outperforms the matching algorithm (BOZORTH3) provided by NIST.