This magic jigsaw puzzle is an example of what I call a 'self-interlocking' geomagic square. The 16 pieces are no longer separated from each other within their cells, but interlock so as to pave a single square area. I had never imagined that such a structure was possible, until an examination of the geometrical analogues of certain algebraic magic squares forced their existence upon me. The visual harmony of the square is a reflection of the symmetries to be found in the algebraic magic square upon which it is based.