Non-heme iron(III) complexes of 14-membered tetraaza macrocycles have previously been found to catalytically decompose hydrogen peroxide to water and molecular oxygen, like the native enzyme catalase. Here the mechanism of this reaction is theoretically investigated by DFT calculations at the (U)B3LYP/6-31G* level, with focus on the reactivity of the possible spin states of the FeIII complexes. The computations suggest that H2O2 decomposition follows a homolytic route with intermediate formation of an iron(IV) oxo radical cation species (L.+FeIV==O) that resembles Compound I of natural iron porphyrin systems. Along the whole catalytic cycle, no significant energetic differences were found for the reaction proceeding on the doublet (S=1/2) or on the quartet (S=3/2) hypersurface, with the single exception of the rate-determining O--O bond cleavage of the first associated hydrogen peroxide molecule, for which reaction via the doublet state is preferred. The sextet (S=5/2) state of the FeIII complexes appears to be unreactive in catalase-like reactions.