It depends on the country and currency but there is the SWIFT system, which works like messaging. There is also the SIC and EuroSIC. For SWIFT system as a bank

It depends on the country and currency but there is the SWIFT system, which works like messaging. There is also the SIC and EuroSIC. For SWIFT system as a bank you have an account on the other bank and sends an instruction to decrease your amount and book it to a receiver. If there are more than one bank between them it gets routed but always "own decrease and other bank increase". Only the receiver bank books to the client. This system works because every bank has an account on other banks and you can build up some paths.