The relativistic motion of an isolated two–body system (bound or
unbound) of given lab energy $K^{0}$ in QED is
separated into cms motion and
relative motion. The relative motion equation ${\cal K}_{L}} \psi_{L}
({\bf r}_{L} ) =0$ contains the momentum eigenvalue ${\bf K}$ of the
cms motion. It is greatly simplified by a binary boost to the
atomic rest frame, where $K^{0}$ and ${\bf K}$ appear only in a
Lorentz–invariant combination. This boost is not a product of
single–particle boosts, which are useful only for perturbative
interactions. CPT–invariance is demonstrated, and orthogonality