The first direct search for lepton-flavour-violating decays of the recently discovered Higgs boson (H) is described. The search is performed in the H→μτe and H→μτh channels, where τe and τh are tau leptons reconstructed in the electronic and hadronic decay channels, respectively. The data sample used in this search was collected in pp collisions at a centre-of-mass energy of s=8 TeV with the CMS experiment at the CERN LHC and corresponds to an integrated luminosity of 19.7 fb−1 . The sensitivity of the search is an order of magnitude better than the existing indirect limits. A slight excess of signal events with a significance of 2.4 standard deviations is observed. The p -value of this excess at MH=125 GeV is 0.010. The best fit branching fraction is B(H→μτ)=(0.84−0.37+0.39)% . A constraint on the branching fraction, B(H→μτ)<1.51% at 95% confidence level is set. This limit is subsequently used to constrain the μ–τ Yukawa couplings to be less than 3.6×10−3 .