Sunfire high beam light

I have a 2.2cc 1996 Pontiac Sunfire with 380,000 km on the engine. The problem is the high beam indicator light on the dash board stays on permanently, whenever I start the car and turn low beam lights on. This happens even though I do not switch the high beam lights on. I checked the bulbs and fuse and they are ok. Please help me to correct this problem. Your help is greatly appreciated.