Is this on a CRT monitor? If so, try a "degauss". If this doesn't work, I am a firm believer in "percussive maintenance", so give it a light but firm slap on the side or the top of the monitor. If that still doesn't work, one of the cathode rays maybe on the fritz and the only resolution then is to put your hand in your pocket and buy a new monitor.
PLEASE don't hit it if it's a TFT monitor!