This paper constructs a number of possible core measures of annual inflation using Singular Spectrum Analysis (SSA). Annual inflation is decomposed into its trend, oscillating and noise components in order to develop an understanding of the trend and cyclicality in South African headline inflation. Five cyclical components are identified with differing amplitude and frequency. The trend and cyclical components of inflation are found to be a good approximation of core inflation, the inertial part of inflation. These core measures are compared to other candidate core measures based on the properties of a good core inflation measure. Generally, the SSA measures outperform commonly use measures of core inflation.