In the present work, we demonstrated a new method of graphene films transferring applying a marker-frame instead of polymer-like films as a support. This method is an alternative that is much faster, cheaper and freely available to all. Our technique guarantees cleaner graphene surface and no polymer residues on it. Consequently, it significantly increases the applicability of graphene. For instance, one can think of using graphene as a component of nanocomposites or coupling it with other nanomaterials. As an example we showed graphene films suspended on GaN nanowires. The characterization of the properties of graphene transferred following the enhanced frame method was performed by Raman spectroscopy, as well as by carrying out SEM imaging and conducting TEM investigations.