  The algebraic formulation of discrete $P$ and $T$ space-time symmetries in
terms of the Dirac algebra is shown to be flawed. This is corrected by relating
these symmetries to fermion quantum numbers defined by a $Cl_{3,3}$ sub-algebra
of the $Cl_{7,7}$ Clifford Unification algebra. A new {\it Conservation Law} is
formulated to the effect that fermion decays and interactions conserve all
seven quantum numbers defined by $Cl_{7,7}$. This can be applied in the design
of high energy experiments and the qualitative interpretation of their results.
