In this paper we carry out unit root tests on real exchange rates recursively as in Caporale et al (2003), but, following Arghyrou and Gregoriou (2007), we adjust the residuals for non-normality using a wild bootstrap method. The results are striking: the correction for non-normality dramatically increases the rejection percentages of the unit root null, and attenuates the erratic behaviour of the t-statistic, thus providing strong evidence in favour of PPP, and suggesting that such a correction might at least go some way towards solving the “PPP puzzle”