These adorable Anthology Fabric napkins (Bari J. for Art Gallery Fabrics) were made simply using one stitch on my Janome 9900 Memory Craft. And it's a stitch many machines have! Look for your satin stitches (this was number 12 on my machine.
To stablilze the fabric I used strips of Sharon Schamber's "Secret" foundation paper which I got from Purple Daisies Quilting. Cristy, Sharon's daughter is a good friend of mine and alerted me to this product many years ago. It's the best ever product for embroidery and applique as well. I simply glue basted 3/4" strips along each edge.
I cut my fabric to 12.5" squares and stitched all the way around, one edge at a time. I didn't try to stop and start at a particular point on each edge. I just made sure at some point the stitches criss-crossed. Which is why you want to do one edge at a time. Do not try to pivot at each corner.
When you finish all the edges, use a tiny applique scissors to cut to but not through all the scallops. Then tear the backing right off.
Is the cutting a touch tedious? Yes. But not difficult. Just a little time consuming. If you're like me and your eyes are an issue be sure to use good light and your best readers!