We have shown that by using three equivalent different techniques (the transfer matrix method, the correlated walks` theory and the partition point technique) for a lattice gas model in one dimension with alternate nearest neighbor ferromagnetic interactions we can find a new equation of the enzyme kinetics. This equation in the limit of no interaction between sites reduces to the classical Michaelis-Henri equation, while for the same interaction between sites reduces to another equation, which we have obtained before. This new equation can be useful for the experimental investigation. (author). 16 refs, 3 figs.