An algorithm is described for retrieving vertical profiles of a non-LTE radiator (lower and upper state densities) and temperature from a spectrally resolved profile of infrared limb radiance. The limb radiance profile integrated over an optically thin line or region of the spectrum can be expressed as an Abel integral equation that may be solved for the vertical profile of volume emission rate. The volume emission rate profiles thus obtained from two or more thin spectral lines or regions representing a single species are used to solve for the vertical profiles of translational temperature and excited state molecular density. These two solutions and the limb radiance profile for nonthin spectral lines or regions are used in a nonlinear recursion scheme to obtain the species vibrational temperature profile. Results obtained in a numerical simulation using the &ngr;2 band of CO2 are presented to demonstrate the method and, in particular, the convergence properties of the relaxation technique for recovery of vibrational temperature.