A theoretical study of the ‘walk’ rearrangement in bicyclo[2.1.0]pentene and perfluorotetramethyl (Dewar thiophene) exo-S-oxide has been carried out. Despite the differences between them, the results for both reactions show an enhancement of aromaticity in the transition state, which is consistent with a pericyclic behavior. NBO calculations show that the small activation energy for the second reaction can be interpreted in terms of a strong stabilization of the transition state by the exo-oxide substituent. So, the mechanism proposed in the past should be revised.