Advanced Replication: in a Master-to-master setup, how to retire old master and make subordinate mas

I have been upgrading a materialized view system. I created the new system in parallel and did master-to-master replication between the old system's master and the upgraded system's master. I upgraded individual materialized-view nodes one by one.

Now all the nodes have been upgraded and are in production, hanging off the new master. The last task in shutting down the old system is to retire the old master. I'm posting this question just to get an idea of what the overall high-level steps are. The old server is the master-master in the replication relationship between the old and new masters. It seems to me I can't just take it off line or de-rez it because the whole multilayer replication scheme ultimately comes back to the old master as its definition point.