I want to install Ubuntu on a removable hard driver, so that when I remove the hard drive and turn on my computer, there exist no signs of Ubuntu (I mean no grub or something else). But when I connect my hard drive and turn on my computer, Can boot from external hard drive and start an Ubuntu session. I want Ubuntu to be installed on my external hard drive,creating a live Linux is not my answer. any suggestions?
Yes, you can. Create a LiveCD and install.
The easiest way to install is to unplug your internal hard drive, plug in your USB hard drive, and install on the Hard Drive with the LiveCD.
Otherwise, you will have to do "something else", and create a swap, data, and home partition manually.
Make sure to install Grub on the hard drive, not your internal hard drive.