Banknotes are processed using a machine equipped with a number of modules by which predetermined numbers of notes are ordered in bundles secured with at least one band and then transferred to a unit to be strapped in groups; an intermittently driven conveyor equipped with pockets operates in conjunction with the modules to direct the bundles in a predetermined succession, according to a previously established sequence, toward a stacker located at an outfeed end of the conveyor. The bundles are stacked in set numbers to form groups in which the predetermined succession is maintained as the single bundles pass along a stacking axis, preserving an initial sequence of code and serial number with which the banknotes are fed initially into the bundling modules.