A search for γγ decays of a Higgs boson is performed in the data sample collected at LEP with the ALEPH detector between 1991 and 1999. This corresponds to an integrated luminosity of 672pb −1 at centre-of-mass energies ranging from 88 to 202GeV. The search is based on topologies arising from a Higgs boson produced in association with a fermion pair via the Higgs-strahlung process e+e−→Hf f ̄, with f f ̄=ν ν ̄,e+e−,μ+μ−,τ+τ− or q q ̄. Twenty-two events are selected in the data, while 28 events are expected from standard model processes. An upper limit is derived, as a function of the Higgs boson mass, on the product of the e+e−→Hf f ̄ cross section and the H→γγ branching fraction. In particular, a fermiophobic Higgs boson produced with the standard model cross section is excluded at 95% confidence level for all masses below 100.7GeV/c2.