The subject matter of this study was the processing of arterial blood oxygen saturation data (SaO 2). The aim was to investigate the downsampling procedure of the SaO 2 records on a broad range of scales. The object of study was a small data set (20 subjects, about 164 seconds duration, sampling rate 300 Hz) borrowed from the well-known portal of medical databases Physionet. The tasks to be solved are a test of the dataset heterogeneity, downsampling of the SaO 2 series and its increments in a broad range of possible, checking the randomness of SaO2 series increments, argumentation in favor of applying the theory of Levy-type processes to the SaO 2 increments and proving of their self-similarity, the definition of the geometrical fractal and its Hausdorff dimension. The methods used are the Levy-type processes theory, statistical methods, boxes-covering method for fractal structures, the autocorrelation function, and programming within MAPLE 2020. The authors obtained the following results: the dataset comprises three subsets with different variability; the records and their increments remain scale-invariant if the switching frequencies remain lower than the reduced sample rate; the increments of SaO 2 records are a Levy-type and self-similar random process; the fractal is the set of positions of the non-zero increments (switch-overs) from a geometrical viewpoint. Conclusions. The scientific novelty of the results obtained is as follows: 1) the fractal nature and the self-similarity of SaO 2 records and their increments were proved for the first time; 2) authors found the fractal Hausdorff dimensions for the subsets in the range (0.48… 0.73) in dependence on variability; 3) authors found the principal possibility of the SaO 2 data sizes essential reducing without losses of vital information.