A method is described that uses target transformation factor analysis techniques to determine the number of independently variable components and recover the spectral end-members present in a set of mixed spectra. These techniques were tested on two sets of synthetic spectral mixtures and several subsets of Thermal Emission Spectrometer (TES) data. In both synthetic mixture sets, the correct numbers of components were determined, and the original spectral end-members were accurately recovered. An initial application of this method was used with several subsets of TES apparent emissivity spectra that contain only minor surface spectral components. This method has demonstrated that the spectra can be modeled using linear combinations of three spectral end-members: atmospheric dust (with atmospheric gas absorptions that vary in unison with the dust shape), water ice cloud, and blackbody. The atmospheric dust and water ice cloud spectral shapes were recovered from several orbits with a wide variety of atmospheric dust opacities during the southern spring and summer seasons. The atmospheric dust spectral shape is nearly constant except for the relative contribution of atmospheric gasses that vary in unison with the dust shape. The water ice spectral shape is also constant with the exception of a small shift in the position of the ~800 cm-1 absorption that was observed during a period of high opacity. ¿ 2000 American Geophysical Union