Atmospheric ozone plays an important role in the biosphere’s absorbing of dangerous solar UV radiation and its contributions to the Earth’s climate. Nowadays, ozone variations are widely monitored by different local and remote sensing methods. Satellite methods can provide data on the global distribution of ozone and its anomalies. In contrast to measurement techniques based on solar radiation measurements, Fourier-transform infrared (FTIR) satellite measurements of thermal radiation provide information, regardless of solar illumination. The global distribution of total ozone columns (TOCs) measured by the IKFS-2 spectrometer aboard the “Meteor M N2” satellite for the period of 2015 to 2020 is presented. The retrieval algorithm uses the artificial neural network (ANN) based on measurements of TOCs by the Aura OMI instrument and the method of principal components for representing IKFS-2 spectral measurements. Latitudinal and seasonal dependencies on the ANN training errors are analyzed and considered as a first approximation of the TOC measurement errors. The TOCs derived by the IKFS-2 instrument are compared to independent ground-based and satellite data. The average differences between the IKFS-2 data and the independent TOC measurements are up to 2% (IKFS-2 usually slightly underestimates the other data), and the standard deviations of differences (SDDs) vary from 2 to 4%. At the same time, both the analysis of the ANN approximation errors of the OMI data and the comparison of the IKFS-2 results with independent data demonstrate an increase in discrepancies towards the poles. In the spring–winter period, SDDs reach 8% in the Southern and 6% in the Northern Hemisphere. The technique presented can be used to process the IKFS-2 spectral data, and as a result, it can provide global information on the TOCs in the period of 2015–2020, regardless of the solar illumination and the presence of clouds.