Abstract The MEG II experiment, based at the Paul Scherrer Institut in Switzerland, reports the result of a search for the decay $$\upmu ^+ \rightarrow {\textrm{e}}^+ \upgamma $$ μ + → e + γ from data taken in the first physics run in 2021. No excess of events over the expected background is observed, yielding an upper limit on the branching ratio of $${\mathcal {B}} (\upmu ^+ \rightarrow {\textrm{e}}^+ \upgamma ) < 7.5 \times 10^{-13}$$ B ( μ + → e + γ ) < 7.5 × 10 - 13 (90% CL). The combination of this result and the limit obtained by MEG gives $${\mathcal {B}} (\upmu ^+ \rightarrow {\textrm{e}}^+ \upgamma ) < 3.1 \times 10^{-13}$$ B ( μ + → e + γ ) < 3.1 × 10 - 13 (90% CL), which is the most stringent limit to date. A ten-fold larger sample of data is being collected during the years 2022–2023, and data-taking will continue in the coming years.