The Federal University of the Southern Border is one of the 18 federal public universities created since 2003 in Brazil. The creation of UFFS, in a border region, is part and result of a unique process that can be considered sui generis among public universities and within of the history of Brazilian higher education. UFFS incorporates the notion of the border (territory, society and culture) in its own name, the reason why it was taken as empirical reference for the purposes of this article. This article intends to describe the implementation experience of the UFFS in order to understand how a university localized in the border region conceives itself and relates with the issues and problems of its surroundings. The description and analysis will focus in particular on the conception and the implementation of the graduate program.