The structure of membrane proteins specifies their functional properties, which are important for medicine and pharmacology and, therefore, is of significant interest. The repetition of transmembrane regions that consist of hydrophobic amino acids is a characteristic and organic feature of polytopic membrane proteins. The ordered repetition (periodicity) can be detected by the Fourier method applied to a digital image of the symbolic amino acid sequence of a protein. In the present work, this investigation was carried out for 24 transmembrane proteins (successfully for 14 of them). If the repetition of transmembrane regions is aperiodic, it can be revealed by another method, that is, the method of the reiterated (four to five times) averaging of the protein hydrophobicity function in a window within the limits of 9-11 amino acids that moves along the sequence. This novel method was applied to the 24 transmembrane proteins (successfully for 19 of them) and demonstrated higher suitability than the Fourier method for predicting the secondary structure of these proteins and the corresponding functional properties.