The problem of the double bond flipping interconversion of the two equivalent ground state structures of cyclobutadiene (CBD) is addressed at the multireference average-quadratic coupled cluster level of theory, which is capable of optimizing the structural parameters of the ground, transition, and excited states on an equal footing. The barrier height involving both the electronic and zero-point vibrational energy contributions is 6.3 kcal mol -11, which is higher than the best earlier theoretical estimate of 4.0 kcal mol-1. This result is confirmed by including into the reference space the orbitals of the CC σ bonds beyond the standard π orbital space. It places the present value into the middle of the range of the measured data (1.6-10 kcal mol-1). An adiabatic singlet-triplet energy gap of 7.4 kcal mol-1 between the transition state 1Btg and the first triplet 3A2g state is obtained. A low barrier height for the CBD automerization and a small ΔE(3A2g, 1B1g) gap bear some relevance on the highly pronounced reactivity of CBD, which is briefly discussed.