  We consider a bipartite generalization of the Curie-Weiss model in a critical
regime. In order to study the asymptotic behavior of the random vector of the
total magnetization we apply the change of variables that diagonalizes the
Hessian matrix of the pressure functional associated to the model. We obtain a
new vector that, suitably rescaled, weakly converges to the product of a
Gaussian distribution and a distribution proportional to $\exp(-\xi x^{4})$,
where the positive constant $\xi$ can be computed from the pressure functional.
