We report results of a population synthesis model that follows the evolution of single and binary stars. In this model, we include the two He white dwarfs merger channel, suggested by Han et al., for the formation of extreme horizontal branch (EHB) stars. The physical parameters of the resulting EHB stars are derived from the Bag of Stellar Tracks and Isochrones data base by Pietrinferni et al., and are thus realistic and observationally supported. The predictions of this model are in good agreement with traditional population synthesis models, except when the spectrum of the stellar population is dominated by binary stars or their products, e.g., EHB stars in the ultraviolet (UV) of early-type galaxies (ETGs). We reproduce successfully the observed colour–magnitude diagram and spectral energy distribution of the metal-rich open cluster NGC 6791. The stellar population in this cluster may be archetypal of the stellar population in ETGs that show the UV excess phenomenon. Our models should be appropriate to study the UV upturn in ETGs.