Most of fingerprint identification systems perform matching algorithms based on different minutiae details present in the fingerprint. Usually, minutiae are extracted from the thinned fingerprint image. Due to the image noise and different preprocessing methods, the thinned image could results in a large number of false minutiae which may decrease the performance of the system. In this paper, some existing algorithms from different studies were integrated to build Automated Fingerprint Identification System. A new matching algorithm was proposed based on feature with two points; minutiae and ridge point. In addition, each feature extracted assigned to an appropriate weight according to proposed weights table. The modified system was tested on FVC2002 DB1 set-A and all four FVC2004 set- A databases and showed that it is effective and gives excellent results that exceed the performance of classic minutiae-based matching algorithm.