  The process $e^+e^- \rightarrow N\bar N$ is studied nearby a threshold with
account for polarizations of all initial and final particles. The nucleon
polarization $\bm \zeta^N$ reveals a strong energy dependence due to that of
the nucleon electromagnetic form factors $G_E(Q^2)$ and $G_M(Q^2)$ caused by
the final-state interaction of nucleons. It is shown that the modulus of the
ratio of these form factors and their relative phase can be determined by
measuring $\bm \zeta^N$ along with the differential cross section. The
polarization degree is analyzed using Paris $N\bar N$ optical potential for
calculation of the form factors. It turns out that $|\bm \zeta^N|$ is high
enough in a rather wide energy range above the threshold. Being especially high
for longitudinally polarized beams, $|\bm \zeta^N|$ is noticeable even if both
$e^+e^-$ beams are unpolarized.
