An apparatus to prevent strip material from falling off the edges of a strip material package when unwinding. The package comprises a generally cylindrical and flangeless core around which the strip material is wound transversely in a plurality of overlapping layers. The apparatus also includes an idler roller. When unwinding, the strip material goes around the idler roller, then around the package, generally in its central portion and then again around the idler roller before being fed to a laminating machine. A method to use the apparatus is also provided.