The Mexican Stitch has become the name of at least two different stitches. Both can be used as decorative stitches and one can be used when pieces two pieces of fabric together (known as faggoting).
Mexican Stitch No. 1
Information on this stitch was found in an embroidery book dated 1900. It defines this stitch as a fine Blanket Stitch and is used occasionally to outline a pattern (see illustration below). It makes an effective outlining stitch in connection with conventional work.
Click on picture to see more detail.
Mexican Stitch No. 2
The following information about this stitch was obtained from an embroidery guide dated 1910.
This stitch can be used to join two pieces of material, as faggoting is so frequently employed, but this stitch is newer and different. It isn’t necessary to use it always for joining stitch. It looks just as pretty when it is worked on top of the material as a decorative band.
Click on picture to see more detail.
To work:
Take a stitch about a sixteenth of an inch long on one edge, then cross straight over and take a stitch of the same length of the other edge. Cross back and forth like this until three straight lines are laid in, then carry the fourth line to the center of the space, and work four buttonhole stitches over the three threads. Finish the fourth thread, then begin all over again, catching he threads together with every fourth thread.
The instructions provided did not include how to use it as a simple decorative stitch, obviously assuming that the embroiderer would understand to use imaginary lines in place of the edges of the material for placement of the stitches.