Based on the phase space generating functional of the Green function f
or a system with a singular higher-order Lagrangian, the quantal conse
rved laws (QCL) have been derived under the global symmetry transforma
tion in the extended phase space. The application of the results to no
n-Abelian higher-derivative Chern-Simons theories (NAHDCST) is studied
; the quantal BRS conserved quantity and conserved angular momentum ar
e obtained. This quantal conserved angular momentum differs from class
ical Noether one.