Remove one border without affecting others

I'm using Excel 2003.

I have a column containing cells all with a right-hand border and some with bottom borders. Something like:

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How can I highlight the whole column and remove only the right-hand border? If I reset everything to no borders then I have to go through an re-do all the bottom borders.

Ah, I never knew that it worked like that. I notice that if one or more cells don't have the given border, then the button won't be highlighted and it will just add to those cells without one. You have to make sure all of the selected cells have the border.

Thanks!