Well, tell us how many miles you have on the bike, general history of the bike, how long have you had it etc ?
My guess is Fartblood is right, i had a similar thing happen a couple years ago, but it was also sputtering at lower RPM's as well.
I took it to the shop told the man clean the carbs, put in brand new jet kit, get it running right. Cost a bit of money, but if you don't know how to work on carbs it might be worth it. Summer is a good time to get it done, I got mine done in winter and had to take apart and re-adjust later because it didn't want to behave correctly in warm weather.
Like Fartblood said it could be the voltage regulator going bad also, the VR's on the FZR's are notorious for dying for no apparent reason, I had mine replaced years ago, but still watch for problems. These things can cause the bike to act totally erratic, just idling, starting, or at any random RPM's, they can also melt wires, blow fuses, you name it. Fortunately I was lucky and it just acted retarded, didn't melt anything. As soon as it was replaced acted like a brand new bike... no problems. Of course it's possible you have something else wrong, but for $75 you can get a new VR and see if that works. If not, try the carbs / jet kit etc.
sorry for the long reply.
