Fingerprint Recognition System is made up of Off-line treatment and On-line treatment; the one is registering all the information of there trieving features which are retrieved in the digitalized fingerprint getting out of the analog fingerprint through the fingerprint acquisition device and the other is the treatment making the decision whether the users are approved to be accessed to the system or not with matching them with the fingerprint features which are retrieved and database from the input fingerprint when the users are approaching the system to use. In this paper, we propose a new data structure, called Union and Division, for processing binarized digital fingerprint image efficiently. We present a minutiae extraction algorithm that is using Union and Division and consists of binarization, noise removal, minutiae extraction stages.