The magnetic properties of a class of 1-D pi -systems having a frontier half-filled band (HFB) of degenerate non-bonding MOs (NBMOs) localized within the elementary units (EU) have been studied theoretically. The localization of the MOs, determined by the topology of the pi -fragments which form the EUs is explained by means of the extended Coulson-Rushbrooke-Longuet-Higgins theorem, The perfect localization and non-overlapping of the NBMOs results in vanishing of the direct (Hund-) and the kinetic exchange interaction between the impaired electrons, The indirect exchange of the impaired electrons (spin polarization exchange) occurs via the delocalized pi -electrons in the filled energy bands.