Financial development is an important component of economic development. In particular, it is very important for developing countries to converge to developed countries in terms of financial development level. In this study, the convergence of the financial development indicators of the Fragile Five Countries to the average of the indicators of the four selected countries (USA, England, Australia and Japan) in the top ten in terms of financial development level for the period 1980-2020 is tested. In addition, stochastic convergence based on relative financial indicator figures, that is, convergence to the mean, is also investigated. The data used in the study were accessed from the World Bank official database. Stationarity test which is introduced to the literature by Nazlıoğlu and Karul (2017) based on the Fourier stationarity test developed first by Becker et al. (2006). This test allows for gradual structural changes and cross-section dependence and cross-section heterogeneity. As in all stationarity tests, the basic hypothesis of this test is that the series is stationary, while the alternative hypothesis claims that it contains a unit root. This test gives results for both the individual and the panel as a whole. As a result of the tests, it is seen that the financial development indicators of the Fragile Five Countries do not converge to the selected country group and its average.