Previous theoretical calculations have predicted normal bond lengths for the pivot cyclobutane bond (C1-C1’) and abnormally long lengths in the hinge bond (C1-C2) of the neutral [2+2] C-60 dimer (1). This result did not agree with the theory that the orbital-interaction-through-bond of pi-sigma-pi type enhanced by strain should elongate the mediating a bond. The orbital interaction through the pivot bond of 1 was indeed detected by the analysis of MO energy levels. Hence the present case offers the first definitive evidence against the bond elongation theory. Instead, we present a universal, parabola-like relation between the lengths (r) of the symmetrical C-q-C-q bond in 1, and other head-to-head cage dimers, and the s-character in the sigma orbital localized at the bond. The relation found here explains all the previously observed lengths of pivot bonds in the head-to-head cage dimers including 1.