A direct search for lepton flavour violating decays of the Higgs boson (H) in the H →eτand H →eμchannels is described. The data sample used in the search was collected in proton–proton collisions at √s=8TeVwith the CMS detector at the LHC and corresponds to an integrated luminosity of 19.7fb−1. No evidence is found for lepton flavour violating decays in either final state. Upper limits on the branching fractions, B(H →eτ) <0.69%and B(H →eμ) <0.035%, are set at the 95% confidence level. The constraint set on B(H →eτ)is an order of magnitude more stringent than the existing indirect limits. The limits are used to constrain the corresponding flavour violating Yukawa couplings, absent in the standard model