  We decompose the monthly aa-index of cycles 10-23 using principal component
analysis (PCA). We show that the first component (PC1) is related to solar
cycle, and accounts for 41.5 % of the variance of the data. The second
component (PC2) is related to 22-year Hale cycle, and explains 23.6% of the
variance of the data. The PC1 time series of aa cycles 10-23 has only one peak
in its power spectrum at the period 10.95 years, which is the average solar
cycle period for the interval SC10-SC23. The PC2 time series of the same cycles
has a clear peak at period 21.90 (Hale cycle) and a smaller peak at 3/4 of that
period. We also study the principal component of sunspot numbers (SSN) for
cycles 10-23, and compare mutual behavior of the PC2 components of aa-index and
SSN PCA analyses. We note that they are in the same phase in all other cycles
than Solar Cycles 15 and 20. The aa cycle 20 also differs from other even aa
cycles in its shape, especially in anomalously high peaks during its descending
phase. Even though there is a coherence in the PC2 time series phases of
aa-index and sunspot number, this effect is too small to cause all of the
difference of the shape of even and odd aa cycles. We estimate that 30% of the
shape of the PC2 component of aa-index is due to sunspot number and the rest to
other recurrent events in Sun/solar-wind. The first maximum of aa-data (typical
to odd cycles), during sunspot maximum, has been shown to be related to coronal
mass ejections (CME), while the second maximum (typical to even cycles) in the
declining phase of cycle, is probably related to high-speed streams (HSS). The
last events increase the activity level such that the minimum between even-odd
cycle-pair is always higher than the minimum between succeeding odd-even cycle
pair.
