A recursive algorithm was developed to invert spectrally resolved earth limb radiance profiles representing the non-local thermodynamic equilibrium altitude regime and species/tangent heights that are optically thin. It was used to infer vertical distributions of temperature and excited NO density from data measured by the Spectral Infrared Rocket Experiment in the NO fundamental band near 5.3 &mgr;m. The solution for excited NO density was used to compute atmospheric cooling rates for the 5.3-&mgr;m band and the de-excitation rate constant k0 for the reaction NO*+O→NO+O.