Sorry to resurrect a thread from Page 3 IO540, but no, you're not missing anything. Modern FMC/FMS/INS/GPS systems fly a constant Great Circle between waypoints. None of the previous posts, including my own, alluded to that. Reference was being made to the PRE-FMC/FMS/INS/GPS era when human navigators calculated the Great Circle Track, and broke it into smaller manageable Rhumb line segments.
I've had a fair bit to do with programming the afore-said modern equipment (including Omega), and frankly, don't know of any way to get them to fly a Rhumb line even if you wanted to (I don't know why one would want to). I even fiddled with such a function on one unit in case anyone wanted it, but it was far too messy, changeing Magnetic Variation kept getting in the way.
Regards,
Old Smokey