A search for events with a photon pair arising from the decay of a Higgs boson produced in association with a fermion pair, is performed in 893 pb−1 of data recorded by the ALEPH detector at LEP at centre-of-mass energies up to 209 GeV. No excess of such events is found over the expected background. An upper limit is derived on the product of the e+e−→HZ cross section and the H→γγ branching fraction as a function of the Higgs boson mass. A fermiophobic Higgs boson produced with the Standard Model cross section is excluded at 95% confidence level for all masses below 105.4 GeV/c2.