I have 3 relay MySQL database servers on my small office LAN backing up a
master and 3 more machines backing up each relay (1 each). They are all
replicating all databases and all tables. The master although running fine
is almost eight years old. I'm thinking it's probably time to make one of
the relays the master, but I've never done this before.

I want the new master to have the IP address of the old master 192.168.0.1
.. To make the change I was going to take the master off the LAN and
shutdown mysql on all the machines, change the IP address on the chosen
relay to that of the master 192.168.0.1, then restart mysql on all the
machines. I always refer to the machines by their IP addresses and never by
their hostnames. Once I successfully make the change I was planning on
making the old master a relay since it is still working fine.

Will this plan work ok? Is there a better or easier way?

Thanks for you attention.

Richard