  Solar and heliospheric parameters can depict notable differences between the
northern and southern hemisphere. Although hemispheric asymmetries of some
heliospheric parameters vary systematically with Hale cycle, this is not common
for solar parameters. Also, no physical mechanism exists which can explain
systematic hemispheric asymmetries. We use a novel method of high
heliolatitudes to increase the fraction of one hemisphere in solar 10.7cm radio
fluxes and sunspot numbers. We calculate sets of hemispheric high-latitude
radio fluxes and sunspot numbers with increasing heliographic latitude during
the last 75 years. We also normalise these fluxes by yearly means in order to
study their continuous variation. We find that cycle maximum radio fluxes and
sunspot numbers in each odd cycle (19, 21, 23) are larger at northern high
latitudes, while in all even cycles (18, 20, 22 24) they are larger at southern
latitudes. This alternation indicates a new form of Hale cycle variation in
solar activity. Hemispheric differences at cycle maxima are 15% for radio flux
and 23% for sunspot numbers. The difference is largest during cycle 19 and
smallest in cycle 24. Continuous fluxes depict a Hale cycle in both
hemispheres, with an opposite phase and amplitude of 5% in north and 4% in
south. Hemispheric Hale cycle can be explained if there is a northward directed
relic magnetic field, which is shifted northward. In odd cycles, the northern
hemisphere is enhanced more than the southern hemisphere and, in even cycles,
the northern hemisphere is reduced more than the southern hemisphere. The
decrease of asymmetry during the 7 cycles can be explained if the relic shift
oscillates at the 210-year Suess/deVries period. Gleissberg cycle consists of
one off-equator excursion of the relic. Relic field in the Sun also offers a
possibility for century-scale forecasting of solar activity.
