Your best bet is to create a new file. There is no backup setting which will tell the SQL Server to delete a backup from within the backup. You should instead create a new file each time you backup the database and simply delete the files which are older than you want using the xp_delete_file stored procedure.
A second option would be to create a backup file for each day of the week and overwrite or delete the file each day before backing it up. This will allow you to keep 7 days worth of backups without having to worry about deleting files.