no, if you want links to open up inside the frame, you can't use only CSS and HTML for this. you can either use traditional HTML frames, which isn't a good idea, or you can try using an inline frame: <iframe>. i don't have time to write out any code for you right now, so all i can say is look into it. it'll be a lot easier to setup than regular HTML frames, and you can use CSS to style it. cross-browser compatibility may be an issue, although i'm not sure. it isn't officially part of the HTML standard.
good luck!