RBS has been fined for attempted Libor fiddling, earlier this year paying a total of £390m to settle cases with US and UK authorities.
Meanwhile Lloyds is updating its practices in light of developments across the rest of the sector.
RBS has told its staff to exit all ongoing social chats immediately and not to open any new such discussions.
Any permanent chats and chat rooms involving other banks or competitors are banned, unless there is a good business reason for them to be in use.
Similarly group chats with clients, brokers and other firms are no longer allowed.
On top of those changes, internal chats have to take place on internal systems where they can more easily be monitored.
Similarly Lloyds has stopped staff engaging in multi-party chats unless there is a specific business reason, approval is given by a senior person in the financial markets team and the chat is then supervised.
One on one chats for business purposes are allowed, but the bank said it wants to have an explicit policy in place rather than being forced to react to events as other lenders have.
“We regularly update the policies that set out the standards of behaviour and ethics we expect from our people to ensure they reflect changes in best practice or regulation or due to technological advances,” said a Lloyds’ spokesperson.
“Recent policy updates include explicit rules governing the usage and controls for messaging systems in financial markets.”
The pair join other lenders including Barclays, JP Morgan and Deutsche bank who are believed to have clamped down on traders talking with rivals.