The square is developed by stitching in the round, so the corners become important. 

The first few rows will want to pull outward, so the first 4 rows also become very important.

The corners you can clearly see are a repeat of two groups, alternated. The first corner group is:
-> 3 beads together at the corner, followed by
-> 2 beads together at the corner, followed by
-> 2 beads together at the corner, followed by
-> 1 bead at the corner, followed by
-> no added beads at the corner (you pass the thread through the corner bead)

The second group is the same as the first group with the addition of another round of 2 beads together.

The first 4 rows are necessarily reinforced by passing the thread through be beads twice. If you pull too hard to get the beads close, you just make yourself work harder to jam the next row of beads between the beads in peyote fashion.

-> add 4 beads to the thread and make a circle of the beads by passing the thread through the first added bead.

-> add 4 beads one at a time to the next row in peyote stitch. Stop and arrange the beads to look uniformly distributed. Reinforce the first and second rows by following the peyote thread path and passing through the first and second row beads.

-> starting at a bead in row 2, add 3 beads together in peyote stitch. Use your needle to spread apart the first and last bead. Push the middle bead down to flatten against the first row bead. If you carefully tighten the thread, friction will hold the middle bead down. It usually takes a couple of tries to accomplish this feat. Do this all around the square (circle). If some of the first 3-bead-groups become disconbobulated, as long as the thread length and tension does not change, it can be repaired in the next row.

-> the beads in the row are applied in two rounds. First move to a first corner bead and add 2 beads together for the corner. Bypass the 1 peyote side bead and go through the row 3 beads. After adding the 4 corner beads, add the 1 peyote side bead reinforcing the corner beads just added.

The rest of the square is easy compared to the start. Continue in peyote stitch and follow the pattern for the corner beads.

Bead weaving directions are notoriously difficult, so ask me questions and I’ll tell you no lies.

Cheers.

I have been looking for a forum and for my first (second) post, I would like to introduce my version of the perfect square.

Cheers to all.

https://www.nytimes.com/2024/01/30/fashion/jewelry-beadwork.html

When I come across Chinese made beads in a foreign country, I’m usually still inclined to buying them. I think sometimes it’s the story behind where you found them and the memory behind the beads is more important than the exact country of origin of the bead.