  We exam the validity of the definition of the ADM angular momentum without
the parity assumption. Explicit examples of asymptotically flat hypersurfaces
in the Minkowski spacetime with zero ADM energy-momentum vector and finite
non-zero angular momentum vector are presented. We also discuss the Beig-\'O
Murchadha-Regge-Teitelboim center of mass and study analogous examples in the
Schwarzschild spacetime.
