In this letter, we present a new method for preparing perpendicular end faces in polymer optical fibers on a base of polymethyl metacrylate. Initially, a scratch is circumferentially made around the fiber. Then, the fiber is briefly cooled with liquid nitrogen or liquid nitrogen vapor, and subsequently bent over a curved surface to obtain a perpendicular fracture. We demonstrate a significant improvement in insertion loss for such faces, which are comparable with those of polished fibers.