This paper examines mean reversion in the real exchange rate index of Australia in the presence of structural breaks from 1984:1 till 2009:2. Conventional unit-root procedures have low power when structural breaks in data are ignored. The null hypothesis is examined using a minimum Lagrange Multiplier unit-root test that allows for breaks in level and trend. This unit-root test with two structural breaks is invariant to the magnitude of the breaks. We were able to reject the unit-root null hypothesis and find evidence of mean reversion and hence PPP with structural break points. This is a startling finding reversing results of past works that failed to reject nonstationarity in the data. The corresponding break dates are 1988:2 and 2002:4 respectively and the structural break dates are statistically significant. The estimated break dates mostly correspond to the period of RER instability (1986-1989) and the recovery of the Australian dollar driven by the resources boom (2001-2002).