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 matching between On-line and Off-line treatment, the most important thing is which features we are going to use as the standard. Therefore, we have been using "Delta" and "Core" as this standard until now, but there might have been some deficits not to exist in every person when we set them up as the standards. In order to handle the users who do not have those features, we are still using the matching method which enables us to make up of the spanning tree or the triangulation with the relations of the spanned feature. However, there are some overheads of the time on these methods and it is not sure whether they make the correct matching or not. In this paper, introduces a new data structure, called Union and Division, representing binary fingerprint image. Minutiae detecting procedure using Union and Division takes, on the average, 32% of the consuming time taken by a minutiae detecting procedure without using Union and Division.