Abstract: An invariant random order is a measure on the space of all orders on a group that is invariant under the shift action of the group. 
It is easy to see that on an amenable group, an invariant random order could be invariantly extenеded to an invariant random linear order. It is natural to ask whether this extension property holds for all groups. A first counterexample was obtained recently by Glasner, Lin and Meyerovitch. I will show, starting from their construction, that every non-amenable group has no invariant random order extension property.