A media dispenser has a delivery module for feeding media, a stacking module for stacking the media, which are fed through the delivery module, on a stacking plate, and a delivery clamp module for clamping the media stacked on the stacking module and delivering the clamped media to the customer, and for feeding the media, which the customer did not take out, to the stacking plate. A path through which the media clamped by the delivery clamp module are fed to a reject box is opened by moving the stacking plate of the stacking module. The method comprises the steps of returning the media onto the stacking plate by a clamp assembly, opening a reject slot by allowing a driving plate to be moved by a driving source and the stacking plate to be moved together with the driving plate, and dropping the media as the clamp assembly unclamps the media through the opened reject slot.