In this paper, we describe a new Umkehr algorithm for the estimation of the vertical ozone profile from observations of the umkehr effect of Götz. The algorithm uses new ozone absorption coefficients, which result in a change in the scale of measurement, and their temperature dependence. Better a priori ozone profiles are possible because of the very large increase in the archive of ozone profile measurements. The characterization of the retrieved ozone profiles and the error analysis follow the recipe of Rodgers. The differences between the new algorithm and the old 1964 algorithm are discussed. For both algorithms, only the retrievals for layers 4–8 (1943 km) are suitable for use in ozone trend analysis. For these layers, the retrieval resolution is trivially improved over that in the 1964 algorithm. For other layers, the retrievals either respond mainly to real ozone changes in adjacent or distant layers, or are a function of low-amplitude changes over a very broad range of layers. The effect of atmospheric aerosol on the retrieved profiles has been determined, and found to be generally similar to the effect for the old algorithm, but differing in some details.