The last things to sew on are the four squares. If you pin these squares onto what would be the left side (pictured above) you can sew them the same way as the triangles...without taking them off the machine to turn. Pin the square down using the Points. Make sure that visually this looks squared to the block. The fabric should all line up. When you get to the center, check to make sure that you are right on the seam and turn. Then sew to the outside edge. 
The finished LeMoyne Star block. 
