Depending on how risky you want to be, you could do one of a few things. (I recommend backing up your data no matter which you choose.)
1. Backup your data and do a clean install of your new operating system of choice. (I recommend Debian Wheezy with MATE.) This option is the least risky but the most work.
2. Upgrade Ubuntu from 11.04 to 12.04 (or 12.10 if you wish). I'm not sure if this is a supported upgrade path, but you could always choose the unsafe method of replacing every reference to
natty in
/etc/apt/sources.list and
/etc/apt/sources.list.d with
precise (or
quantal). This method is
mostly theoretically safe and less work than doing a reinstall (if everything works).
3. Upgrade directly from Ubuntu 11.04 to Debian Wheezy with MATE. This is definitely not a supported upgrade path, but should theoretically work. Backup and remove all extra repositories in
/etc/apt/sources.list.d, import the Debian Wheezy Automatic Archive Signing Key (ASC) and MATE ASC, and backup and replace your
/etc/apt/sources.list with the one below. This method is the most risky but definitely the least work (if everything works).
deb http://ftp.us.debian.org/debian testing main contrib non-free
deb-src http://ftp.us.debian.org/debian testing main contrib non-free
deb http://security.debian.org/ wheezy/updates main contrib non-free
deb-src http://security.debian.org/ wheezy/updates main contrib non-free
deb http://repo.mate-desktop.org/debian wheezy main
deb-src http://repo.mate-desktop.org/debian wheezy main