This stem stitch looks sophisticated after being completed. It is not though. It follows a simple stem stitch technique with a little extra loopings between each stitch.

I will work on a slightly curved stitch line to demonstrate this stitch to you. You need to know the stem stitch to be able to do this stitch.

portugese_stem_stitch   portugese_stem_stitch_ 2
Fig 1: We start with a single stem stitch. Bring the needle out through A, take it in through B and out through C.   Fig 2: Now, take the needle under the stitch A-B without pluckign the fabric beneath. Make sure the needle comes out from the left side of the point C, as shown. This makes a loop around the stitch A-B.
portugese_stem_stitch_ 3      portugese_stem_stitch_ 4
Fig 3: Make another similar loop around the stitch A-B, keeping it towards the left of the previous loop. So, we get two loops.   Fig 4: Now, make the next stem stitch. After making both loops, continue to take the needle in through D and bring it out through E. Then, make the two loops. Make sure the loops encircle both A-B and C-D.
portugese_stem_stitch_ 5   portugese_stem_stitch_ 6
Fig 5: Half way through, our portugese stem stitch would look like this. It gives out a complicated look.   Fig 6: A full curved stitch line woud look like this. Observe how the stitch shows up at the two curves.