Abstract We decompose the monthly cosmic-ray data, using several neutron-monitor count rates, of Cycles 19 – 24 with principal component analysis (PCA). Using different cycle limits, we show that the first and second PC of cosmic-ray (CR) data explain 77 – 79% and 13 – 15% of the total variation of the Oulu CR Cycles 20 – 24 (C20 – C24), 73 – 77% and 13 – 17% of the variation of Hermanus C20 – C24, and 74 – 78% and 17 – 21% of the Climax C19 – C22, respectively. The PC1 time series of the CR Cycles 19 – 24 has only one peak in its power spectrum at the period 10.95 years, which is the average solar-cycle period for SC19 – SC24. The PC2 time series of the same cycles has a clear peak at period 21.90 (Hale cycle) and another peak at one third of that period with no peak at the solar-cycle period. We show that the PC2 of the CR is essential in explaining the differences in the intensities of the even and odd cycles of the CR. The odd cycles have a positive phase in the first half and a negative phase in the second half of their PC2. This leads to a slow decrease in intensity at the beginning of the cycle and a flat minimum for the odd cycles. On the contrary, for the even cycles the phases are reversed, and this leads to faster decrease and more rapid recovery of the CR intensity of the cycle. As a consequence, the even cycles have a more peak-like structure. These results are confirmed with skewness–kurtosis (S–K) analysis. Furthermore, S–K shows that other even and odd cycles, except Cycle 21, are on the regression line with a correlation coefficient 0.85. The Cycles 21 of all eight stations are compactly located in the S–K coordinate system and have smaller skewnesses and higher kurtoses than the odd Cycles 23.