A new method of deriving high-resolution top-of-atmosphere spectral radiances in 10 181 bands, over the whole outgoing long-wave spectrum of the Earth, is presented. Correlations between different channels measured by the Infrared Atmospheric Sounding Interfermeter (IASI) on the MetOp-A (Meteorological Operation) satellite and unobserved wavenumbers are used to estimate far infrared (FIR) radiances at 0.5 cm−1 intervals between 25.25 and 644.75 cm−1 (the FIR), and additionally between 2760 and 3000 cm−1 (the NIR – near infrared). Radiances simulated by the line-by-line radiative transfer model (LBLRTM) are used to construct the prediction model. The spectrum is validated by comparing the Integrated Nadir Long-wave Radiance (INLR) product spanning the whole 25.25–3000 cm−1 range with the corresponding broadband measurements from the Clouds and the Earth's Radiant Energy System (CERES) instrument on the Terra and Aqua satellites at points of simultaneous nadir overpass. There is a mean difference of 0.3 W m−2 sr−1 (0.5% relative difference). This is well within the uncertainties associated with the measurements made by either instrument. However, there is a noticeable contrast when the bias is separated into night-time and daytime scenes with the latter being significantly larger, possibly due to errors in the CERES Ed3 Spectral Response Functions (SRF) correction method. In the absence of an operational spaceborne instrument that isolates the FIR, this product provides a useful proxy for such measurements within the limits of the regression model it is based on, which is shown to have very low root mean squared errors. The new high-resolution spectrum is presented for global mean clear and all skies where the FIR is shown to contribute 44 and 47% to the total INLR, respectively. In terms of the spectral cloud effect (Cloud Integrated Nadir Long-wave Radiance – CINLR), the FIR contributes 19% and in some subtropical instances appears to be negative; results that would go unobserved with a traditional broadband analysis.