Ab initio molecular orbital calculations have been performed on the dimerization of cyclobutadiene using the 3-21G and 6-31G* basis sets. Complete active space SCF calculations with an 8-electron 8-orbital active space were carried out. The anti dimerization occurs by either synchronous concerted or asynchronous concerted pathways with nearly identical activation energies. The syn dimerization is highly favored, and this reaction is predicted to have a negative activation energy. There is no synchronous concerted pathway. The stationary points on the syn dimerization surface consist of a degenerate stationary point which can collapse directly to the product in four different ways or collapse to the transition state for the Cope rearrangement.