Cydobutanetetrone, (CO)(4), has a triplet ground state. Here we predict, based on electronic structure calculations, that the B2N2O4 molecule also has a triplet ground state and is therefore paramagnetic; the structure is an analogue of (CO)(4) in which the carbon ring is replaced by a (BN)(2) ring. Similar to (CO)(4), the triplet ground-state structure of B2N2O4 is also thermodynamically unstable. Besides analysis of the molecular orbitals, we found that the partial atomic charges are good indicators for predicting magnetic ground states.