HDMI monitor resolution problem on Dell ST2310/Inspiron 537/Radeon 4350

I'm not getting 1920x1080 resolution on my Dell ST2310 monitor using a Radeon 4350 graphics card using the HDMI output.  I'm getting about 1" black horizontal and vertical black bars.   Strangely, I get perfect 1920x1080 when I use the DVI output from the video card to the monitor.  I've checked the screen resolution setting in Windows 7 and on the monitor and it's 1920x1080 (monitor just says resolution = 1080p).  Does anyone have any advice?