We obtain a general covariant conservation law of energy momentum in c
omplex general relativity by general displacement transformation in te
rms of Ashtekar new variables. The energy is exactly the ADM Hamiltoni
an on the constraint surface on conditions that an appropriate time fu
nction is chosen. The energy momentum is gauge-covariant and commutes
with all the constraints whence they are physical observables. Further
more, the Poisson brackets of the momentum and the internal SU(2) char
ges form a three-Poincare algebra.