A flux-calibrated high-resolution spectrum of the airglow emission is a practical {lambda}-calibration reference for astronomical spectral observations. It is also useful for constraining the molecular parameters of the OH molecule and the physical conditions in the upper mesosphere. We used the data collected during the first technical commissioning of the GIANO spectrograph at the Telescopio Nazionale Galileo (TNG). The high-resolution (R>~50000) spectrum simultaneously covers the 0.95-2.4 micron wavelength range. Relative flux calibration is achieved by the simultaneous observation of a spectrophotometric standard star. We derived a list of improved positions and intensities of OH infrared lines. The list includes {Lambda}-split doublets, many of which are spectrally resolved. Compared with previous works, the new results correct errors in the wavelengths of the Q-branch transitions. The relative fluxes of OH lines from different vibrational bands show remarkable deviations from theoretical predictions: the {DELTA} v=3,4 lines are a factor of 2 and 4 brighter than expected. We also found evidence of a significant fraction (1-4%) of OH molecules with non-thermal population of high-J levels. Finally, we list wavelengths and fluxes of 153 lines not attributable to OH. Most of these can be associated with O_2_, while 37 lines in the H band are not identified. The O_2_ and unidentified lines in the H band account for ~=5% of the total airglow flux in this band.