The evolution of the electromagnetic coupling, α, in the momentum-transfer range 1800 GeV2<−Q2<21600 GeV2 is studied with about 40 000 Bhabha-scattering events collected with the L3 detector at LEP at centre-of-mass energies View the MathML sources=189–209 GeV. The running of α is parametrised as: α(Q2)=α01−CΔα(Q2), where α0≡α(Q2=0) is the fine-structure constant and C=1 corresponds to the evolution expected in QED. A fit to the differential cross section of the e+e−→e+e− process for scattering angles in the range |cosθ|<0.9 excludes the hypothesis of a constant value of α , C=0, and validates the QED prediction with the result: C=1.05±0.07±0.14, where the first uncertainty is statistical and the second systematic.