Trends in the ozone layer remain among the major problems of the atmosphere physics; thus, results of measurements of the ozone altitude distribution (profile), carried out in the same place and via the same method, are very important. This paper presents the results of the statistical analysis of ensembles of ozone profiles obtained from ground-based microwave radiometry data acquired at the P.N. Lebedev Physical Institute over a period of two decades (1996–2017). The data collected show the significant difference between monthly mean statistical parameters of ozone profiles of the decades 1996–2006 and 2007–2017. The main and unexpected result is the drastic decrease in monthly root-mean-square (rms) variances of ozone profiles over Moscow above 30 km in cold months of the decade 2007–2017 (if compared to the variances in the decade 1996–2006) with the maximum fall by 46% at 39 km in February monthly mean variances. The decade change of variances obtained by averaging over all nine months in the analysis (from September to May) has the same decrease with maximum fall by 25% at 38 km. Additionally, significant decade changes were revealed in other monthly mean statistical parameters: probability density of ozone profile variances, inter-altitude covariance and correlation functions, and time covariance and correlation—as well as their frequency spectra. The decade change of the ozone profile obtained by averaging over the nine months appeared much less significant: the decrease by 5.7% at the altitude of 19 km (with 1.5% sampling error), minor decrease by 2.6% (with sampling error 1.5%) in the profile maximum at 37 km, and increases of 1.7% at 28 km and 2.5% at 47 km (with sampling errors 1.7%)—lower and higher of this maximum. In addition to that, the corresponding averaged mean total column (integral) ozone content above 20 km remained practically unchanged: 4.61 g/m2 for decade 1996–2006 as compared to 4.58 g/m2 for 2007–2017. Possible explanations of revealed offsets are proposed and discussed.