The spin-coupled method, which adopts the most general single-configuration model wave function, has been used to investigate the electronic structure of dimethylenepolycyclobutadienes. A triplet "antipair" is localized on each four-membered ring : the spins of the antipairs are coupled in an antiferromagnetic fashion along the chain. Thus, for an even number of cyclobutadiene units the ground state spin multiplicity is singlet, and for an odd number of units it is tripler. The singlet and tripler states become degenerate in a long chain.