Hi Roseann,
This is a beautiful alphabet isn't it?! Really good question, too!
As far as I can tell, the letters were broken up into two sections and/or done in the opposite direction we would normally go. I did a quick example with directional arrows.

Look at the A. This is done in two strokes. The first starts with the "crossbar" and a downward stroke, then loops up and around in a counterclockwise fashion. Then does the loop de loops and finishes at the bottom left. The second stroke starts at the bottom right and finishes at the top (where the circle is).
The B starts and ends at the same place but with two separate strokes.
The C is made in one stroke and literally goes in reverse to what you would normally do.
This is a very intricate alphabet that would take lots of practice and lots of large arm movements so as to avoid shakey lines. I traced the letters but you can still see some line shake. These letters take a GREAT deal of control. But with lots of practice, the results would be very rewarding!