  The Coulomb correction (difference from the 1st Born approximation) to the
Moli\`{e}re screening angle in multiple Coulomb scattering theory is evaluated
with the allowance for inelastic contribution. The controversy between
dominance of close- or remote-collision contributions to Coulomb correction is
discussed. For scattering centres represented by a Coulomb potential with a
generic (not necessarily spherically symmetric) creening function, the Coulomb
correction is proven to be screening-independent, by virtue of the eikonal
phase cancellation in regions distant from the Coulomb singularity. Treating
the atom %more self-consistently, as an assembly of pointlike electrons and the
nucleus, and summing the scattering probability over all the final atom states,
it is shown that besides the Coulomb correction due to close encounters of the
incident charged particle with atomic nuclei, there are similar corrections due
to close encounters with atomic electrons (an analog of Bloch correction). For
low $Z\neq1$ the latter contribution can reach $\sim 25\%$, but its observation
is partly obscured by multiple scattering effects.
