How to Supreme a fruit

Supreming a fruit is the act of cutting off the rind and pith (the bitter white part just underneath the colored rind), and removing the membranes that separate the fruit sections.

To do this:

Cut off a healthy chunk of  the top and bottom of the fruit, so it can stand flat.

Turn it on its end, then cut off the rind, starting from the top and moving downward. Use the cross section as a depth marker - you're looking to remove all the rind and white bit. Don't be afraid of cutting a little deep - it's better to remove all the pith than to leave some on.

Turn the orange on its side and slice down the membrane with your knife, freeing each segment.

Pull the segments free, remove any leftover membrane and enjoy.

Here's a video, because seeing is sometimes the best teacher.