Trace the wire back to its source. I'm guessing this is a ground wire. One end most likely goes to the negative battery terminal, and the other end goes to ground.
The best way to check is to get a copy of the schematic for your bike, and use it to find out where this wire goes. Once we know that, diagnosing what's making it burn will be easier.
Photos might help as well.
Luke M
Used to have a 1979 CB750L, sold it as a parts bike, now riding a slightly modified 1984 VT700C. Network/Field Engineer. Central OH, USA, Earth, Sol System, Milky Way Galaxy, Universe.