  A new version of tetrad gravity in globally hyperbolic, asymptotically flat
at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is
obtained by using a new parametrization of arbitrary cotetrads to define a set
of configurational variables to be used in the ADM metric action. Seven of the
fourteen first class constraints have the form of the vanishing of canonical
momenta. A comparison is made with other models of tetrad gravity and with the
ADM canonical formalism for metric gravity. The phase space expression of
various 4-tensors is explicitly given.
