See what happens if I try to add the trefoils at the end?
Although I do like the way that trefoil reshapes the chains
but you'd have to remove one of the rings to make it fit.
This square motif is from Tatting Book no. 13 by Ann Orr (sadly no date on the booklet). Interestingly there is a paragraph in there about a "new method in tatting" which explains how to make a split ring with "reverse stitches". The explanation says to make the first half of the ring, then take off the hand and turn over (luckily we found we don't need to do that), before making the second side with reverse stitches. I wish there was a date in the book!