  In the Minimal Supersymmetric Standard Model we present the calculation of
the single charged Higgs-boson production in the gamma W- or Z W-fusion and the
charged Higgs strahlung channel, e^+ e^- -> e nu H^\pm. The set of all O(alpha)
corrections arising from loops of Standard Model fermions and scalar fermions
are taken into account. Contrary to the case of single neutral heavy CP-even
Higgs-boson production, for the charged Higgs boson we find for all the
parameter space of the typical benchmark scenarios a cross section smaller than
\sim 0.01 fb for sqrt(s)/2 \lessim M_H^\pm.
