I agree with MrDenny's last comment...
WHY???
Do you ONLY do FULL backups? If not, this will really mess up your backups and restores.
A Differential Backup is of all the changes since the LAST Full backup. A transaction log backup is of everything since the last backup of any kind. Sooooo
At 1 you do a full backup to location A
At 2 you do a transaction log (TL) backup to location A
At 3 you do a full backup to location B
At 4 you do a TL backup to location A
etc...
Once you do a second Full backup (location B), all of the following backups (DIFF or TL) belong to that backup and not to the first Full backup (location A).
So, if you want to do a restore and use LocationA full backup, you will only be able to restore up to the time you did a full backup to LocationB.
So, what's the point? Instead, do what MrDenny suggests...do the backups to one location and COPY the backup files to a new location.
-SQLBill