B3LYP, CCSD(T), and CASPT2 calculations with the 6-311+G(2df) basis set have been performed on the radical anion and radical cation of cyclobutanetetraone (1). The very similar energies computed for the B-2(1g) and (2)A(2u) an A,u states of both 1 center dot(+) and 1 center dot(-) indicate that the singly occupied b(1g) and a(2u) MOS in these two states of the radical cation and anion have nearly the same energies, thus supporting the previously made prediction that neutral 1has a B-3(2u) ground state. Reaction of squaric acid with O center dot(-), followed by negative ion photoelectron spectroscopy (NIPES) on the 1 center dot(-)thus formed, is proposed as an experimental test of the startling prediction that tetraketone (1), a molecule that would be expected to be a closed-shell singlet, actually has a triplet ground state.