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The results of a search for a standard model-like Higgs boson decaying into two photons in the mass range between 70 and 110 GeV are presented. The analysis uses the data set collected by the CMS experiment in proton-proton collisions at root s = 13 TeV corresponding to integrated luminosities of 36.3 fb(-1), 41.5 fb(-1) and 54.4 fb(-1) during the 2016, 2017, and 2018 LHC running periods, respectively. No significant excess over the background expectation is observed and 95% cofidence level upper limits are set on the product of the cross section and branching fraction for decays of an additional Higgs boson into two photons. The maximum deviation with respect to the background is seen for a mass hypothesis of 95.4 GeV with a local (global) significance of 2.9 (1.3) standard deviations. The observed upper limit ranges from 15 to 73 fb.