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The final results of the search for the lepton flavour violating decay$\mu^{+} \rightarrow {\rm e^{+}} \gamma$ based on the full dataset collected bythe MEG experiment at the Paul Scherrer Institut in the period 2009--2013 andtotalling $7.5\times 10^{14}$ stopped muons on target are presented. Nosignificant excess of events is observed in the dataset with respect to theexpected background and a new upper limit on the branching ratio of this decayof $BR( \mu^{+} \rightarrow {\rm e^{+}} \gamma ) < 4.2 \times 10^{-13}$ (90\%\confidence level) is established, which represents the most stringent limit onthe existence of this decay to date.

Search for the Lepton Flavour Violating Decay $\mu^{+} \to e^+ \gamma$ with the Full Dataset of the MEG Experiment