A general covariant conservation law of energy-momentum in complex gen
eral relativity is obtained by way of general displacement transformat
ion in terms of Ashtekar's new variables. The energy is exactly the AD
M Hamiltonian on the constraint surface on condition that an appropria
te time function is chosen. The energy-momentum is gauge covariant and
commutes with all the constraints whence they are physical observable
s. Furthermore, the Poisson brackets of the momentum and the internal
SU(2) charges form a 3-Poincare algebra.