Many of us find handlebar vibration on FZ6 to be quite bad at certain RPMs.
There are many ways to address it.
1. Make sure your handlebar clamps (2 small plates for 06 and older or 1 big plate for 07 and newer) are properly torqued.
Front bolts need to be tightened and torqued first and the top plate should be pushing against upper crown. Then the rear bolts should be tightened and torqued.
2. Grip puppies or aftermarket grips can help soak up good amount of vibration.
3. Heavier bar ends can help. Do a search for "HVMP" and you will find good info on this.
4. There are several ways to add weight to the bar to reduce vibration.. it can be filled with sand or lead shot.