  We present a parameter-free gauge formulation of general relativity in terms
of a new set of real spin connection variables. The theory is constructed by
extending the phase space of the recently formulated conformal geometrodynamics
for canonical gravity to accommodate a spin gauge description. This leads to a
further enlarged set of first class gravitational constraints consisting of a
reduced Hamiltonian constraint and the canonical generators for spin gauge and
conformorphism transformations. Owing to the incorporated conformal symmetry,
the new theory is shown to be free from an ambiguity of the Barbero-Immirzi
type.
