The problem of the existence of two Kekule isomers 1a and 1b of cyclobutadieno-p-benzoquinone is addressed by the CAS(10,10)/6-31G*//GVB(2)/6-31G* and CASPT2(10,10)/ANO(3s2p1d,2s1p)//GVB(2)/6-31G* theoretical models. It is shown that the barrier separating these isomers on the Born-Oppenheimer surface practically disappears if the zero-point vibrational energies are taken into account. The angular strain and antiaromaticity of the more stable isomer 1a are estimated by employing the appropriate homodesmic reactions. It is concluded that 1a should be experimentally isolable, albeit in extreme conditions.