A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7~TeV, and corresponds to an integrated luminosity of 4.8~fb$^{-1}$. Limits are set on the cross section of a standard model Higgs boson decaying to two photons. The expected exclusion limit at 95\% confidence level is between 1.2 and 2.1 times the standard model cross section in the mass range 110$-$150\,GeV. The observed limit excludes at 95\% confidence level a standard model Higgs boson decaying into two photons in the mass ranges 110.0$-$111.0, 117.5$-$120.5, 128.5$-$132.0, 139.0$-$140.0 and 146.0$-$147.0\,GeV. The largest excess of events over the expected background is observed around 125\,GeV. Taking into account the look-elsewhere effect in the search range 110$-$150\,GeV the excess has a global significance of 1.6 standard deviations. More data are required to ascertain the origin of this excess.

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