  It is shown that the well-known triviality of the Einstein field equations in
two dimensions is not a sufficient condition for the Einstein-Hilbert action to
be a total divergence, if the general covariance is to be preserved, that is, a
coordinate system is not fixed. Consequently, a Hamiltonian formulation is
possible without any modification of the two dimensional Einstein-Hilbert
action. We find the resulting constraints and the corresponding gauge
transfromations of the metric tensor.
