The Mexican Square is not widely published, at least not in the books I have or the research I have done. Since it is unusual, it may be the perfect addition to your embroidery fancy work.
The following excerpts are from 1899.
Directions for the Mexican Square.
Begin the square by placing the threads as stamped from A to B. In laying the last thread bring all the threads together and tie at the center, finishing off the thread along the side, which completes the foundation threads. Begin to weave with a knot at the center, weaving over one and under one of the five threads at the corner of the square as numbered until the cross lines C and Dare reached; then fasten the thread and repeat for the next corner.
After the square is finished buttonhole around the edge and cut away the linen.