  In this paper, we use the Killing vector method to formulate the de
Sitter/Anti-de Sitter invariant special relativity (dS/AdS-SR). Through solving
the Einstein equation with $\Lambda\neq 0$, the basic inertial metric for
dS/AdS-SR is determined to be the Beltrami metric $B_{\mu\nu}(x)$. The
corresponding Killing equations are system of ten simultaneous partial
differential equations of first order. Their most general solutions were
obtained, and all the ten independent Killing vectors were found out. These
results confirm that the Beltrami metric has maximal spacetime symmetry. The
ten Killing-Noether charges are obtained. They are energy, momenta, Lorentz
boost and angular momentum in SR-theory with $\Lambda\neq 0$. Consequently,
dS/AdS-SR is consistently established for the vacuum with $\Lambda\neq 0$ via
Killing vector method rather than the unpopular classical domain theory.
