To accurately simulate the present Earth climate requires an atmospheric longwave radiation model whose computed fluxes agree to within ¿1% of the only presently available standard, line by line (LBL) calculations. This standard derives from the agreement to within ¿1% of various LBL calculations (Luther et al., 1988). To model potential future climate change requires an atmospheric longwave radiation model that can easily incorparate many trace gases. To meet these requirements, a longwave band model of 100 cm-1 resolution is presented. Random band model transmissions are modified to account for overabsorption compared to LBL calculations, with empirical cofficients chosen to give good agreement with LBL spectral fluxes. The longwave band model (LWBM) integrated fluxes agree to within ¿1% of LBL fluxes, while heating rates agree to within ¿5%. The LWBM is used in the National Center for Atmospheric Research Community Climate Model Version 1 to compute longwave radiation. It is demonstrated that by not including minor bands of CO2 and O3, other trace gases (CH4, N2O, CFCl3, CF2Cl2), or nonblack surface emissivity effects results in a significant bias in tropical clear-sky outgoing longwave radiation of 8--10 W m-2 over oceans and up to 15 W m-2 over sandy deserts. ¿ American Geophysical Union 1992