  I study the properties of the equilibrium probability distribution of a
protein folding model originally introduced by Wako and Saito, and later
reconsidered by Munoz and Eaton. The model is a one-dimensional model with
binary variables and many-body, long-range interactions, which has been solved
exactly through a mapping to a two-dimensional model of binary variables with
local constraints. Here I show that the equilibrium probability of this
two-dimensional model factors into the product of local cluster probabilities,
each raised to a suitable exponent. The clusters involved are single sites,
nearest-neighbour pairs and square plaquettes, and the exponents are the
coefficients of the entropy expansion of the cluster variation method. As a
consequence, the cluster variation method is exact for this model.
