A number of biomedical data can be investigated using methods of fractal geometry. A measurement of their nonlinear character and chaoticity can be used for subsequent data classification or irregularity detection. In this paper, we introduce the method of the fractional Brownian bridge for the Hurst exponent estimation from a signal and apply it to the electroencephalogram (EEG) data. The technique is used to detect the early stages of Alzheimer’s disease, exhibiting significant performance when compared with control patients. The measures of variability where the most significant changes occur together with the recommended EEG channels are presented in the paper.