  The elliptic system of equations, which is general-covariant and locally
SU(2)-covariant, is investigated. The new condition of the Dirichlet problem
solvability and the condition of zeros absence for solutions are obtained for
this system, which contains in particular case the Sen-Witten equation. On this
basis it is proved the existence of the wide class of hypersurfaces, in all
points of which there exists a correspondence between the Sen-Witten spinor
field and three-frame, which generalizes the Nester orthoframe. The Nester
special orthoframe also exists on a certain subclass containing not only the
maximal hypersurfaces.
