Bevel vertices on a flat plane I imagine there’s an easy fix but at the moment I just don’t have any idea how to do that. 



I made a flat plane, made some loopcuts to divide it and now want the corners to be round. It works for the corners which are "outside" but for the corners which lie "inside" the form it does not work. My aim is that the bevel looks like the red marked curve in my example.

How can I solve that?

Edit:
To make it more clear: when I try to bevel the "inside" vertex I get something like that, but not a curve.
It's dependent on the internal edges.


Starting as shown
X > Limited Dissolve (selected) internal edges
CtrlShiftB Bevel (selected) corner vertices