upgrad pip3 on Ubuntu

I tried to upgrade my pip3 (pip for Python3) on my second Ubuntu system
the same way I have done it before on another system. But it doesn't
work for Python3, only for Python2.

{bash]
user@MONSTER:~$ pip --version
pip 6.0.8 from /usr/local/lib/python2.7/dist-packages (python 2.7)
user@MONSTER:~$ pip3 --version
pip 1.5.4 from /usr/lib/python3/dist-packages (python 3.4)
user@MONSTER:~$ sudo python3 -m pip install pip --upgrade
Requirement already up-to-date: pip
in /usr/local/lib/python3.4/dist-packages
[/bash]

You see, the installed pip3 is 1.5.4 and the online available (and for
python2 still installed) version is 6.0.8.