Why do I have a black lining around my screen?

Well, I have a 23inch LG screen with a max resolution of 1920x1080 and a XFX Radeon HD 6970. Problem is on some games I have a black square around the screen. Like I can see the game and I set the game resolution to 1920x1080, but the game picture is like centerd and there is a black area around the game picture. Is there a setting I have to change? Or what? I set resolutions to 1920x1080 but still no luck. F.E.A.R 3 and Prince of Persia show the same result as well as Crysis 2. Anyone have suggestions?