So to create a square in a square. You start w/your center square and sew Half Square Triangles (HST) to each edge. The tricky part is to make sure that it ends up as a square again. So I like to fold my square in half and pinch each edge at the mid point. I've inserted a pin to show, since the fabric is black. Then I take the triangle and pinch it in half.
Since this triangle was cut w/the NN rulers it has a blunted point, but that's OK just imagine the point is still there and make the other point match up w/the edges. As in the photo.
Then match up the pins or centers. You will have a point hanging off on one end and not the other. Your 1/4" seam should start right where the point starts to hang off the edge, and should finish right off the blunted off point on the other end. See Photo.
Do this w/each edge. Usually I do the two opposite sides, press and then do the other two.
Your finished Square in a Square should be nice and square.