  The spacetime symmetries of SGM action proposed as the gravitational coupling
of N-G fermions are investigated. The commutators of new nonlinear
supersymmetry (NL SUSY) transformations form a closed algebra, which reveals
N-G fermion (NL SUSY) nature and a generalized general coordinate
transformation. A generalized local Lorentz transformation, which forms a
closed algebra, is also introduced.
