A new technique has been developed to obtain the total ozone content (TOC) under cloudy conditions from the spectra of outgoing thermal IR radiation measured by a satellite IRFS-2 spectrometer. Analysis of the technique errors has shown that the differences between the obtained TOC and independent satellite (OMI) and ground-based (Dobson, Brewer, and M-124 instruments) measurements are usually 3-5%. The highest differences (up to 10%) are observed in the southern polar latitudes in the presence of an ozone hole over Antarctica. IRFS-2 allowed the study of ozone miniholes over Russia in the first quarter of 2016. The measurements show an almost twofold decrease in TOC on certain days.