The method of the two neutron monitors was used to analyze the parameters of the rigidity spectrum variations (RSV) of galactic cosmic ray intensity (GCR) flux in solar cycle 24 based on the data from the global network of neutron monitors. This method is an alternative to the least squares method when there are few monitors working stably in a given period, and their use in the least squares method is impossible. Analyses of the changes in exponent γ in the RSV of GCR flux from 2009 to 2019 were studied. The soft RSV (γ = 1.2–1.3) of the GCR flux around the maximum epoch and the hard RSV (γ = 0.6–0.9) around the minimum epoch of solar activity (SA) is the general feature of GCR modulation in the GeV energy scale (5, 50), to which neutron monitors were found to correspond. Therefore, various values of the RSV γ in the considered period show that during the decrease and increase period of SA, the essential changes in the large-scale structure of the heliospheric magnetic field (HMF) fluctuations/turbulence take place. The exponent γ of the RSV of the GCR flux can be considered a significant parameter to investigate the long-period changes in the GCR flux.