We present a new result based on an analysis of the data collected by the MEG detector at the Paul Scherrer Institut in 2009 and 2010, in search of the lepton flavour violating decay mu->e gamma. The likelihood analysis of the combined data sample, which corresponds to a total of 1.8 x 10**14 muon decays, gives a 90% C.L. upper limit of 2.4 x 10**-12 on the branching ratio of the mu->e gamma decay, constituting the most stringent limit on the existence of this decay to date.