A new data analysis software is presented that has been developed for the retrieval of atmospheric minor constituents from limb-sounding observations made in the millimeter and sub-millimeter spectral regions. The code, which is called MARC (Millimetre-wave Atmospheric-Retrieval Code), has been designed to analyze the observations of the MARSCHALS (Millimetre-wave Airborne Receivers for Spectroscopic CHaracterisation in Atmospheric Limb-Sounding) instrument which operates on the M-55 stratospheric aircraft. The main objective of the analysis of MARSCHALS observations will be to assess long-wave measurement capabilities for the study of the upper troposphere and lower stratosphere regions. The key questions will be the accuracy and spatial resolution that can be achieved by long-wave measurements in presence of clouds and horizontal gradients.MARC performs a global-fit multi-target retrieval, in which optimal estimation is used and errors of the forward model parameters are taken into account for the definition of the cost function minimized in the retrieval. With these features it is easy to use the variables of the problem as either forward model constant parameters or retrieved unknowns with minimum impact on the stability of the retrieval. MARC can perform a wide spectral-band analysis of the observations without a selection of the analyzed channels, and the retrieval process provides an error budget of the retrieved unknowns that includes both the forward model errors and the measurement errors. The error budget obtained in this way is smaller than that obtained when accounting a posteriori for the systematic errors. The new combination of the retrieval features makes possible an efficient and optimal exploitation of the information content of the observations.