A revised four-step model based on the reinvestigation of the kinetics of the subsystems is suggested for the description of the dynamics of the iodate-sulfite-thiosulfate reaction. It is shown that the rate equation of the iodate-sulfite reaction contains an undiscovered term that depends on the square of the concentration of the hydrogen ion as an autocatalyst making the reaction "supercatalytic". In contrast to earlier studies but already supposed by a more recent one, the parallel oxidation of thiosulfate by iodate into tetrathionate and sulfite has also been established experimentally as well as the rate coefficients of the parallel pathways. Combining these kinetic studies yields a new model that does riot include the cross-catalytic effect of thiosulfate and the inhibitory effect of sulfite supposed hypothetically by Rabai and Beck to describe the dynamics of the combined system. In fact, the supercatalytic effect of the hydrogen ion on the sulfite-iodate reaction and the HI dependence of the thiosulfate-iodate reaction along with the parallel formation of. sulfite and tetrathionate are sufficient for perfect reflection of all the most important characteristics of the pH-time curves of the composite system. Nevertheless, the revised model significantly decreases the number of the kinetic parameters necessary to simulate the experimental results.