  The dependence of the nucleon polarization in the reaction $e^+ + e^- \to N +
\bar{N} +\pi^0 $ over different invariant variables in frame of the
non-resonant mechanism, has been derived. The nucleon polarization is expressed
in terms of six invariant complex amplitudes, assuming the conservation of the
hadron electromagnetic currents and the P-invariance of the hadron
electromagnetic interaction. An inclusive experimental setup when the proton
(or the antiproton) and the pion are detected in coincidence is considered.
Numerical estimations were performed for the so called normal polarization in
the energy range from threshold up to $s=16$ GeV$^2$, using a specific
parametrization of the nucleon electromagnetic form factors and taking into
account the unpolarized differential cross section of the non-resonant
mechanism, as previously calculated.
