When to transplant peonies?
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www.extension.iastate.edu/news/2009/aug/062801.htm
I have found that it can be true, peonies may not bloom the year after splitting/transplanting. Give them time to acclimate.
http://www.bhg.com/gardening/flowers/perennials/how-to-transplant-peonies/
Large, vigorous plants can be dug and divided for propagation purposes. September is the best time to transplant established peonies. Begin by cutting the peonystems near ground level. Then carefully dig around and under each plant.