If the border is a peel-and-stick border, perhaps pointing a hair dryer on it will softer the glue and you can carefully peel it right off. Just be careful to apply on the miniminal amount of heat because you don't know what's holding the full wallpaper to the wall. IF you soften up the main wallpaper, you'll have a new problem. Just more the hair dryer close to the wallpaper a little at a time until it starts coming off.
If the border is being held by paste glue, the hair dryer method may work too. But if it doesn't, either try to find the mfgr and see what they recommend. Take a sample to a store or find a WEB site of a retailer or company that sells/makes wallpaper/border, and start e-mailing like crazy!
Just remember ... Whatever method you use, be mindful of the main wallpaper and what might happen. Again, you don't want to create a new problem with the main wallpaper whilst solving the problem of your border. My best to ya and hope this helps.