To surpreme an orange is simply the process of removing the peel, pith, seeds, and membranes, which leaves you with clean, sweet orange segments. You may remember that I used orange supremes in the Piña Colada Salsa recipe and we’ll be using them tonight in duck a l’orange. Orange supremes are also delicious in salads. This same process can be used for lemons, limes, or other citrus fruits.
Start with an orange.
Cut off the top and bottom of the orange.
Use a knife to cut off the peel and any white pith.
You should be able to clearly see the membranes between the segments.
Carefully cut the segments from between the membranes.
Repeat the process until all orange segments are removed.
The Gourmand Mom 
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Yours is the way I make orange supremes although this morning on another web site (it was Finecooking.com) the suggestion was that one peels the orange, as you do, then separate it in half with your fingers, then cut the membranes from the center outward. I haven’t tried it and don’t know if it is more trouble or not. Personally I think cutting inward as you describe and then turning the knife in the center of the orange lets you peel out the supreme quite easily. This way there is less waste of the actual orange segment.