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The aim of the paper is to examine the mean reversion in health expenditure of 45 sub-Saharan African countries. The series on current health expenditure (percent of GDP in total), obtained from the World Development Indicators, each spanned the years 2000–2017. We employed the Fourier unit root test, which allows modelling structural breaks, to deal with any such breaks that could arise as a result of a small sample size (18 years) of data available on health expenditure of the selected countries. The results showed evidence of mean reversion in the health spending pattern of 27 sub-Saharan African countries. There is evidence of nonmean reversion in the health expenditure pattern of the remaining 18 countries considered. We further investigate the link between health expenditure and health outcome, using infant mortality rate and under-five mortality rate as health outcome variables. An inverse association could be observed between the infant mortality rate and health expenditure and between the under-five mortality rate and health expenditure in 24 sub-Saharan African countries. On the other hand, in 13 other sub-Saharan African countries we observed a positive association between the variables. The findings of this study could be of great importance to healthcare delivery programmes in the studied countries.