The stability of the singlet and triplet states of tetraoxocyclobutane (C4O4, the tetramer of carbon monoxide) has been investigated at various levels of theory. Second-order perturbation favors the singlet state, whereas the triplet and open-shell singlet states are computed to be more stable using the hybrid B3LYP density functional method. High-level CCSD(T) calculations reveal the perturbation theory to be insufficient, whereas the B3LYP method provides both qualitatively and quantitatively reliable results.