This study offers a new unit root test procedure that is based on the combination of Fourier ADF and Fourier KSS unit root tests by using Fisher's statistics. The main advantage of this approach is that it is a useful method, especially in cases where the findings obtained from the two test methods differ. In this paper, we investigate the mean-reverting properties of the real exchange rate series for seven fragile economies. Fourier ADF and Fourier KSS tests results point to different findings. When the combination unit root test is applied, it is confirmed that the real exchange rate series are stationary for four fragile economies, namely Brazil, India, Indonesia, and Mexico.