An extended version of the Zwanzig-Lauritzen model, in which each fold
contributes with a random energy, is discussed. By means of the repli
ca trick, an exact solution is achieved for a variant of the general m
odel proposed. Its solution shows that the second order phase transiti
on between the folded and the extended phase, exhibited by the Zwanzig
-Lauritzen model, disappears when a random energy term - depending onl
y on the number of folds of the chain - is added.