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A measurement of the mass of the Higgs boson in the diphoton decay channel is presented. This analysis is based on 35.9fb-1 of proton-proton collision data collected during the 2016 LHC running period, with the CMS detector at a centre-of-mass energy of 13 TeV. A refined detector calibration and new analysis techniques have been used to improve the precision of this measurement. The Higgs boson mass is measured to be mH=125.78±0.26GeV. This is combined with a measurement of mH already performed in the H->ZZ->4[l] decay channel using the same data set, giving mH=125.46±0.16GeV. This result, when further combined with an earlier measurement of mH using data collected in 2011 and 2012 with the CMS detector, gives a value for the Higgs boson mass of mH=125.38±0.14GeV. This is currently the most precise measurement of the mass of the Higgs boson.