Dig a hole about 4 inches deep with a garden trowel or shovel. Liatris is not picky about soil, but it should be well drained. Improve clay and other hard soils by mixing compost or soil conditioner into the bottom of the hole.
Cut to the ground any stems remaining from the previous year and clear debris from the site.
Dig around and under a group of blazing star so you have a clump with the roots intact. If you want smaller clumps, break it apart with your hands or a trowel. Keep as much soil on the clumps as possible.
Transplant each clump to a new hole so that the soil level remains the same as in the old location.
Backfill the hole with the amended, excavated soil. Tamp gently with your hands.
Water thoroughly to settle the soil and cover the planting area with an inch of mulch to conserve moisture. Water for a few months until the clumps are established.
Clean up the site by moving the excess soil from the new site to the old planting hole.