  The paper search for the minimum of the entropy of a two- dimensional
distribution in the Fr\'echet class, the class of distributions with given
marginals. The main result for discrete distributions is an algorithm for
building the minimizing distribution, which is given by the maximum
distribution function of the Fr\'echet class after a suitable rearrangement of
the rows and of the columns. For absolutely continuous distributions a minimum
does not exists, and the infimum is equal to -\infty.
