Originally complied for 1868-1967 and subsequently continued so that it now covers 150 years, the aa index has become a vital resource for studying space climate change. However, there have been debates about the inter-calibration of data from the different stations. In addition, the effects of secular change in the geomagnetic field have not previously been allowed for. As a result, the components of the ''classical'' aa index for the southern and northern hemispheres (aa S and aa N) have drifted apart. We here separately correct both aa S and aa N for both these effects using the same method as used to generate the classic aa values but allowing d, the minimum angular separation of each station from a nominal auroral oval, to vary as calculated using the IGRF-12 and gufm1 models of the intrinsic geomagnetic field. Our approach is to correct the quantized a K-values for each station, originally scaled on the assumption that d values are constant, with time-dependent scale factors that allow for the drift in d. This requires revisiting the intercalibration of successive stations used in making the aa S and aa N composites. These intercalibrations are defined using independent data and daily averages from 11 years before and after each station change and it is shown that they depend on the time of year. This procedure produces new homogenized hemispheric aa indices, aa HS and aa HN , which show centennial-scale changes that are in very close agreement. Calibration problems with the classic aa index are shown to have arisen from drifts in d combined with simpler corrections which gave an incorrect temporal variation and underestimate the rise in aa during the 20th century by about 15%.