Raise the arm up and look for a retainer clip on the bottom side nearest the pivot point. I believe this is how yours is removed.
To remove the door handle from a BMW z4 you will need to have special tool or a hook tool to grab the slider and pull it towards you to release it.
The 2013 BMW Z4 has 16 valves.
The 2006 BMW Z4 has 24 valves.
The 2007 BMW Z4 has 24 valves.
The 2012 BMW Z4 has 16 valves.
The 2005 BMW Z4 has 24 valves.
The 2009 BMW Z4 has 24 valves.
The 2008 BMW Z4 has 24 valves.
The 2011 BMW Z4 has 24 valves.
The 2010 BMW Z4 has 24 valves.
The 2014 BMW Z4 has 16 valves.
The 2003 BMW Z4 has 24 valves.