  We present a new calculation, in the nonrelativistic QCD (NRQCD)
factorization formalism, of the relativistic corrections to the
double-charmonium cross section sigma[e+ e- -> J/psi+eta_c] at the energy of
the Belle and BABAR experiments. In comparison with previous work, our
calculation contains several refinements. These include the use of the improved
results for the nonperturbative NRQCD matrix elements, the resummation of a
class of relativistic corrections, the use of the vector-meson-dominance method
to calculate the fragmentation contribution to the pure QED amplitude, the
inclusion of the effects of the running of alpha, and the inclusion of the
contribution that arises from the interference between the relativistic
corrections and the corrections of next-to-leading order in alpha_s. We also
present a detailed estimate of the theoretical uncertainty. We conclude that
the discrepancy between the theoretical prediction for sigma[e+e- ->
J/psi+eta_c] and the experimental measurements has been resolved.
