The catalytic mechanism of the non-heme iron extradiol dioxygenases has been studied using hybrid density functional theory. These enzymes cleave a C-C bond outside the two hydroxyl groups of catechols, in contrast to the intradiol enzymes which cleave the C-C bond between these two groups. The chemical models used comprise about 70 atoms and include the first-shell ligands, two histidines, one glutamate, and one water, as well as some second-shell ligands, two histidines, one aspartate, and one tyrosine. Catechol is found to bind as a monoanion in agreement with experiments, while dioxygen is found to replace the water ligand. A spin-transition from the initial septet to a quintet state prepares the system for formation of a bridging peroxide with the catechol substrate. When the O-O bond is cleaved in the suggested rate-limiting step, a key substrate intermediate with partly radical and partly anionic character is formed. The partly anionic character is found to determine the selectivity of the enzyme. The results are compared to available experimental information and to previous studies.