  Ionization of highly charged relativistic ions by neutral atoms and ions is
considered. Numerical results of recently developed computer codes based on the
relativistic Born and the equivalent-photon approximations are presented. The
ionization of the outer shells dominate. For the outer projectile electron
shells, which give the main contribution to the process, the non-relativistic
Schr\"odinger wave functions can be used. The formulae for the non-relativistic
reduction of the Dirac matrix-elements are obtained for ionization of electrons
with arbitrary quantum numbers $n$ and $\ell$.
