  We calculate two-photon exchange amplitude for the elastic electron-proton
scattering in the framework of dispersion relations. The imaginary part of the
amplitude is determined by unitarity. Since in the unitarity relation
intermediate states are on shell, off-shell form factors are not needed for the
calculation. The real part is then evaluated using analytical properties of the
amplitude. The expression for the elastic contribution to the amplitude,
obtained in our approach, differs from the results of traditional calculations
with on-shell form factors. Nevertheless, numerically the difference is minor
for Q^2 up to 6 GeV^2.
