  A canonical analysis of the first-order two-dimensional Einstein-Hilbert
action has shown it to have no physical degrees of freedom and to possess an
unusual gauge symmetry with a symmetric field $\xi_{\mu\nu}$ acting as a gauge
function. Some consequences of this symmetry are explored. The action is
quantized and it is shown that all loop diagrams beyond one-loop order vanish.
Furthermore, explicit calculation of the one-loop two-point function shows that
it too vanishes, with the contribution of the ghost loop cancelling that of the
``graviton'' loop.
