  The chiral Lagrangian including more than two spin-3/2 fields becomes complex
in general when the self-dual connection satisfies its equation of motion, and
the imaginary part of the chiral Lagrangian gives the additional equation for
spin-3/2 fields which gives rise to the inconsistency. This inconsistency can
be removed by taking the tetrad to be complex and defining the total Lagrangian
which is the sum of the chiral Lagrangian and its complex conjugate. It is
possible to establish the right (left)-handed supersymmetry in its total
Lagrangian as in the case of the chiral Lagrangian. We also comment on the
canonical formulation of the total Lagrangian.
