Yes, the ECB has adopted replacement rules for damaged or mutilated (e.g. partially burnt, cut, discoloured or decomposed) banknotes, which are uniformly applied by all national central banks of the Eurosystem. The rules are laid down in a public ECB Decision which defines the criteria to be met if you present a damaged banknote for exchange.

This Decision also contains the rules for the exchange of euro banknotes damaged by anti-theft devices, also called intelligent banknote neutralised systems (IBNS). In essence, banknotes damaged by IBNS can only be exchanged at the request of the original owner, or its appointed agent, who has become victim of the crime.