The time to transplant peony plants is in the fall, cutting the stems down in September or whenever the plant's foliage starts to die. It is very important to be careful with the root system, so dig carefully around the plant, starting 8 to 10 inches from the center. Dig under the plant as well, angling the spade toward the plant so the roots come up in a clump.
Carefully pick up the clump of roots, and gently shake off any loose soil. It is not necessary to divide, but if dividing into separate plants is desired, now is the time. To divide, slice through the roots in a number of sections, ensuring to keep three to five of the large, nodule shaped shoots, or eyes, in each section.
Prepare the new bed for the peonies in a sunny, well-draining area. Space holes 3 feet apart if planting more than one peony plant. The eyes and roots must be planted no more than 2 inches under ground and facing upward. Peony plants do not thrive when buried too deep in the ground.
Fill in the hole, again ensuring not to cover the roots with more than 2 inches of soil. Water thoroughly. Newly transplanted peony plants may not bloom in the first spring or even until the third or fourth year.