Trading between 2 counterparties

#1
Hi,

I have a query regarding trading.When 2 traders/mktmakers agree upon a price and confirm a trade between themselves, how do they execute it on the exchange.What if their orders get matched with passive orders already sitting in the order book.
Would they book on a different set of order book like a negotiated order book where they can identify the counter party with whom they want to match the order and based on this the trade gets matched on the exchange?Pls confirm.

Best Regds
Siva