We investigate the synchronization of the Eurozone’s government bond yields at different maturities. For this purpose, we combine principal component analysis with random matrix theory. We find that synchronization depends on yield maturity. Short-term yields are not synchronized. Medium- and long-term yields, instead, were highly synchronized early after the introduction of the Euro. Synchronization then decreased significantly during the Great Recession and the European Debt Crisis, to partially recover after 2015. We interpret our empirical results using portfolio theory, and we point to divergence trades as a source of the self-sustained yield asynchronous dynamics. Our results envisage synchronization as a requirement for the smooth transmission of conventional monetary policy in the Eurozone.