A search is performed for heavy Majorana neutrinos (N) using an event signature defined by two like-sign charged leptons of the same flavour and two jets. The data correspond to an integrated luminosity of 5.0 inverse femtobarns of pp collisions at a centre-of-mass energy of 7 TeV collected with the CMS detector at the Large Hadron Collider. No excess of events is observed beyond the expected standard model background and therefore upper limits are set on the square of the mixing element, abs(V[ell N]) squared, for ell = e, mu, as a function of Majorana neutrino mass. These are the first direct upper limits on the heavy Majorana-neutrino mixing for m[N] > 90 GeV.