A narrow band model is presented to simulate the transfer of infrared radiation through a cloudless nocturnal boundary layer. The absorption and emission by the rotational and vibrational lines of water vapor, carbon dioxide and ozone in the spectral region from 0--2800 cm-1 is modeled with the Goody band model, while the absorption of the water vapor continuum in the atmospheric window region is evaluated from the empirical formulas of Roberts et al. (1976). To approximate the integration of the absorption coefficient, over the inhomogeneous path, the Curtis-Godson method is used, and to approximate the integration over all zenith angles a diffusion factor of 5/3 independent of path length is adopted. It is shown that in the troposphere the results of the narrow band model diverge from cooling rate calculations performed by line-by-line models by about 0.2 K d-1 (~20%). Moreover, from a comparison with 44 observations of downward flux at the surface, it is shown that the simulated flux underestimates the observed flux by about 6 W m-2 (~2%). ¿ American Geophysical Union 1990