This stitch is a version of Romanian couching which is suitable for small or narrow areas.  It consists of laid stitches each of which are couched down with a single small diagonal stitch using the same thread, together they form a central ridge down the stitched area.  This is a form of self-couching.

Historically, it is likely that this stitch is a development of Romanian couching: the earliest known examples date from 17th century England, whereas self-couching generally goes back centuries.  The main difference between the two stitches are that this version has a single couched stitch anchoring each laid stitch, and those couched stitches form a slightly raised line; Romanian couching normally has multiple couching stitches holding down each laid stitch and their position is not stipulated.

This stitch is first documented in the early 20th century.  Louisa Pesel lists it as “oriental or Roumanian stitch”, saying that “the name is unsatisfactory, as it is neither the most common nor the only stitch found in work from the orient. Nevertheless, it is so generally accepted that to rename it would lead to confusion.”