  Her X-1/HZ Her is one of the best studied accreting X-ray pulsars. In
addition to the pulsating and orbital periods, the X-ray and optical light
curves of the source exhibit an almost periodic 35-day variability caused by a
precessing accretion disk. The nature of the observed long-term stability of
the 35-day cycle has been debatable. The X-ray pulse frequency of Her X-1
measured by the Fermi/GBM demonstrates periodical variations with X-ray flux at
the Main-on state of the source. We explain the observed periodic
sub-microsecond pulse frequency changes by the free precession of a triaxial
neutron star with parameters previously inferred from an independent analysis
of the X-ray pulse evolution over the 35-day cycle. In the Fermi/GBM data, we
identified several time intervals with a duration of half a year or longer
where the neutron star precession period describing the pulse frequency
variations does not change. We found that the NS precession period varies
within one per cent in different intervals. Such variations in the free
precession period on a year time scale can be explained by <1% changes in the
fractional difference between the triaxial neutron star's moments of inertia
due to the accreted mass readjustment or variable internal coupling of the
neutron star crust with the core.
