In this paper, we use the concept of real convergence (considering the stationarity of per capita cross-country output differences) and present updated evidence on the persistence properties of output differential data, accounting for the potential occurrence of persistence changes. We focus on per capita output differences for 14 Eurozone countries over the period 1950-2015. Results suggest that the gap between the central and northwestern countries has been reduced through persistent convergence paths. However, the convergence path of the southern countries to the central and northern countries seems to have been interrupted.