An apparatus for processing embroidery data for forming an embroidery on a workpiece by a sewing machine, including an image reader for reading an original embroidery image to generate original embroidery image data, an outline generator for generating an outline of the original embroidery image from the original embroidery image data, a device for determining whether the outline should be changed so as to enlarge at least one area partially defined by the changed outline, a device for changing the outline according to the determination of the determining device, and a stitch data generator for generating stitch-position data representative of stitch positions defining the embroidery to be formed within the changed outline.