Recently it was pointed out that for the evaluation of the numerically dominant pion-exchange contribution to the hadronic light-by-light scattering correction in the muon g-2, a fully off-shell pion-photon-photon form factor should be used. Following this proposal, we first derive a new short-distance constraint on the off-shell form factor which enters at the external vertex for the muon g-2 and show that it is related to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints. With a value for the magnetic susceptibility as estimated in the same large-N_C framework, we obtain the result a_{mu}(LbyL; pi^0) = (72 pm 12) x 10^{-11}. Updating our earlier results for the contributions from the exchanges of the eta and eta-prime using simple vector-meson dominance form factors, we obtain a_{mu}(LbyL; PS) = (99 pm 16) x 10^{-11} for the sum of all light pseudoscalars. Combined with available evaluations for the other contributions to hadronic light-by-light scattering this leads to the new estimate a_{mu}(LbyL; had) = (116 pm 40) x 10^{-11}.
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