  We study the biharmonic equation $\Delta^2 u =u^{-\alpha}$, $0<\alpha<1$, in
a smooth and bounded domain $\Omega\subset\RR^n$, $n\geq 2$, subject to
Dirichlet boundary conditions. Under some suitable assumptions on $\o$ related
to the positivity of the Green function for the biharmonic operator, we prove
the existence and uniqueness of a solution.
