Keeping in mind Select - Modify - Border involves feathering, which I almost never want so I don't use Border...
Does it have to be relative to the current selection size? If so, does Contract not work? If not, Select - All then Select - Modify - Border again comes to mind.
Select - Inverse, then Select - Modify - Expand, then Select - Inverse again also could be an alternative you could experiment with, for example if you're recording an action.
-Noel