The nucleus-independent chemical shifts (NICS) and electron density profiles along the inner and outer regions defined by the two stacked aromatic rings of [2.2]paracyclophane have been analyzed and compared to those of free benzene and p-xylene and benzene dimers taken as reference models. It is found that stacked aromatic rings show a reduction of the NICS indicator of aromaticity as compared to the same free aromatic systems. This decrease of the NICS values upon stacking is not due to an increase of the electron density in the inner region between the rings (as claimed in a previous work) but is related to the magnetic couplings between superimposed rings that affect this measure of local aromaticity. The increase of local aromaticity in superimposed aromatic rings indicated by NICS is not real but the result of the coupling between the magnetic fields generated by the two stacked rings. This result warns about the use of NICS as a descriptor of aromaticity for species having superimposed aromatic rings.