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Peonies are propagated by dividing the crown (the underground mass of the plants). Unless a peony is at least a vigorous, 3 year old plant, it probably doesn't have a crown large enough for division.
In the fall, prepare the site where you plan to locate the new plants first, because the divisions should be transplanted right away. Dig up clumps, and cut them with a sharp knife into pieces with at least 3 "eyes" each. The "eyes" are growing points on the crown. Transplant the divisions at least 3' apart. The eyes must be no deeper than 1-2" below the soil surface, or they won't grow. It's hard to explain these parts and processes without illustrations, so if it sounds confusing, find a book on plant propagation, perennials, or peonies, and that should help. Enjoy!
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