Use su to become the user who is running dropbox and download/install the newest version.

su -s /bin/bash username
cd ~ && wget --no-check-certificate -O - "https://www.dropbox.com/download?plat=lnx.x86" | tar xzf -

Then you can check the daemon using

~/.dropbox-dist/dropboxd

Also, may need to upgrade the the DAEMON environment variable in /etc/init.d/dropbox

More information at https://www.dropbox.com/install?os=lnx