A transfer-matrix formalism is introduced to evaluate exactly the partition function of the Muñoz-Eaton model, relating the folding kinetics of proteins of known structure to their thermodynamics and topology. This technique can be used for a generic protein, for any choice of the energy and entropy parameters, and in principle allows the model to be used as a first tool to characterize the dynamics of a protein of known native state and equilibrium population. Applications to a beta-hairpin and to protein CI-2, with comparisons to previous results, are also shown.