  The rate for the production of a pair of massive fermions in $e^+ e^-$
annihilation plus real or virtual radiation of a pair of massless fermions is
calculated analytically. The contributions for real and virtual radiation are
displayed separately. The asymptotic behaviour close to threshold and for high
energies is given in a compact form. These approximations provide arguments for
the appropriate choice of the scale in the ${\cal O}(\alpha)$ result, such that
no large logarithms remain in the final answer.
