The energy profiles of the isomerization of mono, di-, and tetracyano-substituted cyclobutadienes (CBDs) are computed at the multireference average quadratic coupled cluster/complete active space self-consistent field level of theory. It was found that the energy barrier heights for the automerization reaction are 2.6 (tetracyanoCBD), 5.1 (1,3-dicyano-CBD), and 6.4 (cyano-CBD) kcal mol-1, implying that they are lowered relative to that in the parent CBD (6.4 kcal mol-1), the monosubstituted derivative being an exception. Since the free CBD shuttles between two equivalent structures even at low temperature of 10 K, it follows that bond-stretch isomerism does not take place in cyanocyclobutadienes. Instead, these compounds exhibit rapid fluxional interconversion at room temperature between two bond-stretch isomers by the double bond flipping mechanism. The reason behind the decrease in the barrier heights is identified as a slightly enhanced resonance effect at the saddle points separating two (equivalent) bond-stretch isomers, compared to that in the equilibrium structures, predominantly due to the diradical character of the former. It is also shown that the energy gap between the singlet ground state saddle point structure and the first triplet equilibrium geometry decreases upon multiple substitution by the cyano groups. The splitting of the S and T energy is small being within the range of 6.5-8.2 kcal mol-1.