  We discuss hadronic light-by-light scattering contribution to the muon
anomalous magnetic moment a_\mu^{\rm lbl}, paying particular attention to the
consistent matching between the short- and the long-distance behavior of the
light-by-light scattering amplitude. We argue that the short-distance QCD
imposes strong constraints on this amplitude overlooked in previous analyses.
We find that accounting for these constraints leads to approximately 50 per
cent increase in the central value of a_\mu^{\rm lbl}, compared to existing
estimates. The hadronic light-by-light scattering contribution becomes
a_\mu^{\rm lbl}=136(25) \times 10^{-11}, thereby shifting the Standard Model
prediction closer to the experimental value.
