How do I install Ubuntu to another partition from Ubuntu with Unetbootin?
Basically Unetbootin wiki says to create a temp partition to install the live to, then install your real ubuntu in another partition and finally wipe your temporary one.
Another way to go, suggested there, would be going for the net-inst image which loads into RAM and leaves your hd free to be mounted or umounted.
Not to mention the link already provided by @Anwar Shah How to install Ubuntu from within other Linux Distributions without reboot