A measurement of the mass of the Higgs boson in the diphoton decay channel is presented. This analysis is based on 35.9 fb(-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 m(H) = 125.78 +/- 0.26GeV. This is combined with a measurement of m(H) already performed in the H -> ZZ -> 4l decay channel using the same data set, giving m(H) = 125.46 +/- 0.16GeV. This result, when further combined with an earlier measurement of m(H) using data collected in 2011 and 2012 with the CMS detector, gives a value for the Higgs boson mass of m(H) = 125.38 +/- 0.14GeV. This is currently the most precise measurement of the mass of the Higgs boson. (C) 2020 The Author(s). Published by Elsevier B.V.