The process $e^+e^- rightarrow Nbar N$ 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 $Nbar N$ 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.
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