This Aleutian hat band or belt is very, very finely woven.  The form and the exceptional quality of weave are extremely rare.  Aleutian twining was noted by early basketry collectors as being "as fine as linen". This is certainly an example that matches that description.

The Aleuts lived in an extremely difficult climate off the coast of Alaska.  The women collected the long rye grass during the warm summer months and then set it aside to dry.   Weaving took place during the long, cold winter. The grass was completely hand twined and then embroidered with silk acquired from Russian traders. If you look closely at the twining, you will see that the weaver has used plain twining and also twining with a twist which creates open work. She surely was a master weaver.