To put it another way...on the headband there are two plastic parts. One looks like a link to join two sections and the other plastic part looks like and is a buckle. Unbuckle it
If you take some of the tension out of the strap you can see the double sewn end. It's double looped back. Just take the tension off and unthread the double sewn end.
It is hard to put this into words but hopefully this has gotten you close enough to figure it out. Once you see that double sewn end you'll figure out how to undo it.