Unlike the surface couching, where the couching thread sits on the surface of the fabric, the underside couching technique allows it to pass through the fabric and hide under the fabric.
Visually, it might end up looking like the backstitch. Now, underside couching was used during medieval times in Ecclesiastical embroidery or church embroidery, where metallic threads were used often. Since it was tricky to pull the metallic threads in and out of the fabric, it was probably much easier to couch it down and hide the couching thread on the reverse of the fabric. The technique is pretty much similar to what a machine does when stitching.

This stitch can be used to fill up portions of the pattern, as it was used to in various medieval embroideries. I will use simple cotton floss to illustrate this stitch, and work over a curved line to show how easily this stitch can meander.

underside_couching_1 underside_couching_2
Fig 1: Start by bringing out a thread (brown in the illustration) for laying from one end of the stitch line. Keep it open.
Now, bring another thread (red in the illustration) out, on the stitch line, as shown. 
Fig 2: Now, keep the laid thread over the stitch line and roll it over to the side slightly. Anchor the laid thread down with the couching thread, but pass the needle through the point that you brought it out from, as shown.  
underside_couching_3 underside_couching_4
Fig 3: Now, pull the couching thread from the reverse side till the laid thread is fastened as shown.  Fig 4: Now, with a slight tension, keep pulling the couching thread till it disappears into the fabric, pulling the laid thread with it. 
underside_couching_5 underside_couching_6
Fig 5: Continue with this method for the entire stitch line. A finished underside couching row would look like this. Fig 6: The reverse side of the fabric would look like this- more like a surface couching!
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