  We consider a specific Hamiltonian formulation of the Teleparallel Equivalent
of General Relativity, where the canonical variables are expressed by means of
differential forms. We show that some ``position'' variables of this
formulation can be always gauge-transformed to zero. In this gauge the
constraints of the theory become simpler, and the other ``position'' variables
acquire a nice geometric interpretation that allows for an alternative, clearer
form of the constraints. Based on these results we derive some exact solutions
to the constraints.
