unetbootin is a 32bit app, so you need to go multilib first (if you haven't already) to run it under 64bit.
after I think this should do:
from a normal user terminal window (under X)
$ xhost +localhost
$ su -
# file unetbootin-linux-549
unetbootin-linux-549: ELF 32-bit LSB executable, Intel 80386, version 1 (GNU/Linux), statically linked, stripped
# chmod +x unetbootin-linux-549
# export DISPLAY=localhost:0.0
the xhost is to allow connection from localhost to the X display and the export for root is to connect at the first local display: that's because you have to run an X app as root under an X session owned by your user.
it's worth to mention that there are also tools to run directly applications as root that use polkit, like kdesu under kde or (the one I'm using) gksu-polkit (needs vala and libgee).
EDIT: sorry for the question, just curiosity: what do you use unetbootin for?