  A first-order Lagrangian $L^\nabla $ variationally equivalent to the
second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian
depends on a symmetric linear connection, but the dependence is covariant under
diffeomorphisms. The variational problem defined by $L^\nabla $ is proved to be
regular and its Hamiltonian formulation is studied, including its covariant
Hamiltonian attached to $\nabla $.
