How to Prevent Protruding Corners on Pillows

Nothing says that you must have square corners on a pillow. You can round off the pillow corners without making an actually round pillow. This works especially well on a pillow that you are sewing a piping or cording edge. In most cases you will need to clip the cording's seam allowance when you are sewing to allow the cording to smoothly go around the corner. (How to Cover Cording to Create Your Own Piping)
The simplest template to round off a corner is a kitchen plate. Be sure to create the same round corner on all four corners by either folding the cover to cut all four corners at the same time, or creating a paper template to repeat the corner on each corner of the pillow.