This pulled thread stitch consists of a grid of squares, each double stitched which gives a regular pattern of raised lines and square holes.  All of the vertical stitches are worked first and then the horizontal ones are added to fill in the square grid.  Unlike four-sided stitch this stitch forms true squares rather than slanted ones.

Some authors work each stitch once rather than twice into the same holes which will give a less open effect.  For a version worked only once and also with a small gap between each square, see framed cross filling.

This stitch is sometimes used to work the background for Madeira embroidery, hence it’s alternative names of arrendado and crivo (crivo translates as sieve).  N.B. both of these alternative names can be used for pulled thread work generally in Madeira work, not always this stitch.  Some Madeiran sources indicate that some warp and weft threads should be removed before the stitch is worked in order to create a more open effect.

The name punch stitch is presumably from the the term ‘punch work’ which is an alternative name for pulled thread work.  It arose from the appearance of the holes which typify the technique which resemble punched holes.