We study the relative efficiency of the sovereign debt and its credit default swap (CDS) market during the European sovereign debt crisis in years 2010 to 2013. The empirical results indicate that the no-arbitrage condition between the two markets holds in the long run. However, the return to the no-arbitrage condition is extremely slow. The price discovery mechanism is in the CDS market for the relatively tranquil countries, but not always in the CDS market for the countries most severely influenced by the crisis. This finding does not support banning naked CDS considered by the Eurozone monetary authority.