The determinant treated in this note came up in a recent investigation of computer-blurred pictures by D. SLEPIAN [l]. The problem was to determine when the original picture can be uniquely reconstructed from the blurred picture. In the mathematical model the picture is a n x m matrix of nonnegative integers. The blurring is a replacement of each entry by a weighted average of the elements in some specified neighborhood of that entry. One of the most simple (but fundamental) cases led to the following determinant.