  We analyse the most general connection allowed by Einstein-Hilbert theory in
Palatini formalism. We also consider a matter lagrangian independent of the
affine connection. We show that any solution of the equation of the connection
is essentially Levi-Civita up to a term that contains an undetermined 1-form.
Finally, it is proved that these connections and Levi-Civita describe a
completely equivalent physics.
