Context. The recurrent nova RS Ophiuchi undergoes nova eruptions every 10-20 years as a result of thermonuclear runaway on the surface of a white dwarf close to the Chandrasekhar limit. Both the progress of the eruption and its aftermath depend on the (poorly known) composition of the red giant in the RS Oph system. Aims. Our aim is to understand better the effect of the giant secondary on the recurrent nova eruption. Methods. Synthetic spectra were computed for a grid of M-giant model atmospheres having a range of effective temperatures 3200 < Teff < 4400 K, gravities 0 < log g < 1 and abundances -4 < [Fe/H] < 0.5, and fit to infrared spectra of RS Oph as it returned to quiescence after its 2006 eruption. We have modelled the infrared spectrum in the range 1.4-2.5µm to determine metallicity and effective temperature of the red giant. Results. We find Teff= 4100 ±100 K, log g = 0.0 ±0.5, [Fe/H] = 0.0 ±0.5, [C/H] = -0.8 ±0.2, [N/H] = +0.6 ±0.3 in the atmosphere of the secondary, and demonstrate that inclusion of some dust ""veiling"" in the spectra cannot improve our fits.