Upgrade from 5.4.3 to the latest version on a DL with two core servers

Like many others I'm going to need to upgrade from 5.4.3 to the latest version sometime in the next few months.  We run two DL4000 with replication between the two.  How do I go about it?  I've read the how to upgrade from 5.4.x to 6.x doc so as I understand it I do the target box first?  So do I do all the steps in the "upgrading cores" section of the Doc on the target then run the RUU and then do the same thing and run the 6.1.2 updater?  Then once that is done repeat on the source core?  I could do with it not going wrong as our target core is at a site about 300 miles away!