grub configuration, boot.

[Dj YB]

hello,

I have been trying to look over many solutions and tutorials with no luck.
my goal was and still is, to clone my internal 40GB hard-drive which contain 
fc11 on to my external usb-hard-drive 500GB.
aftar many tutorials I finally used Clonezilla.
that worked great and the hdd is cloned.
the problem is that the boot configurations are the same, and so when I boot 
from the usb-hdd I actually run from the internal hdd.
and now for the question.
since this usb-drive is meant to be able to boot on every computer,
I can I config grub to boot (run) the OS in the same drive it is being loaded 
from?

for example:
my current setup is that the fc11 internal drive is sdb and the usb-hdd is sde
and the same grub is (clone) on both drives.

any help is very appreciated.
thanks
YB.