  Long observational series for bipolar active regions (ARs) provide
significant information about the mutual transformation of the poloidal and
toroidal components of the global solar magnetic field. The direction of the
toroidal field determines the polarity of leading sunspots in ARs in accordance
with the Hale's polarity law. The vast majority of bipolar ARs obey this
regularity, whereas a few percent of ARs have the opposite sense of polarity
(anti-Hale ARs). However, the study of these ARs is hampered by their poor
statistics. The data for five 11-year cycles (16-18 and 23,24) were combined
here to compile a synthetic cycle of unique time length and latitudinal width.
The synthetic cycle comprises data for 14838 ARs and 367 of them are the
anti-Hale ARs. A specific routine to compile the synthetic cycle was
demonstrated. We found that, in general, anti-Hale ARs follow the solar cycle
and are spread throughout the time-latitude diagram evenly, which implies their
fundamental connection with the global dynamo mechanism and the toroidal flux
system. The increase in their number and percentage occurs in the second part
of the cycle, which is in favour of their contribution to the polar field
reversal. The excess in the anti-Hale ARs percentage at the edges of the
butterfly diagram and near an oncoming solar minimum (where the toroidal field
weakens) might be associated with strengthening of the influence of turbulent
convection and magnetic field fluctuations on the arising flux tubes. The
evidence of the misalignment between the magnetic and heliographic equators is
also found.
