What I found was that I could ease my fingers under the edge of the frame where the fabric goes into the frame. Look closely and you'll see where the two halves join together. If you force your fingers under, you can very gradually loosen the two halves and begin the process of pulling it apart.

For the record, it probably took me a good 30 minutes to get it completely apart, but I was also being way paranoid that I'd either (1) snap the frame in half, or (2) poke through the fabric.

It's a gradual process - if you just try and manhandle it apart it won't work. Just slowly work your way around the frame, prying and loosening a bit each time, and eventually the two halves will pop apart...