The Swiss operation of Coutts is being probed by the German authorities on alleged aiding of client tax evasion.
Current and former employees of Coutts in Switzerland are being probed, RBS, which owns Coutts, said in its annual results.
The statement added that the bank is cooperating with the investigators.
RBS CEO Ross McEwan said: "I want to be very clear if we find anything that has evidence of wrong doing we will come down incredibly hard on any of those issues.
"Any situation like this we take seriously. This is what has tarnished the banking industry and in my view private banks have taken far too long to catch up with the public’s expectations," he added.