A direct search for lepton flavour violating decays of the Higgs boson (H) in the (H\to e\tau ) and (H\to e\mu ) channels is described. The data sample used in the search was collected in proton–proton collisions at (\sqrt{s}=8\text{TeV}) with the CMS detector at the LHC and corresponds to an integrated luminosity of 19.7 fb(^{−1}). No evidence is found for lepton flavour violating decays in either final state. Upper limits on the branching fractions, (B\left(H\to e\tau \right)<0.69\text{%}) and (B\left(H\to e\mu \right)<0.035\text{%}), are set at the 95% confidence level. The constraint set on (B\left(H\to e\tau \right)) 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.