Shari: Wysteria do not divide or transplant well. HOWEVER, wysteria is an easy plant to get starts off of using either cuttings or layering (rooting a stem to create a new plant). The University of Missouri Extension has a great web publication on the "Home Propagation of Garden and Landscape Plants". One of the plants that is discussed is the wysteria. You can find this publication by going to the following URL: http://muextension.missouri.edu/explore/agguides/hort/g06970.htm
I hope this helps you and have fun with your wysteria.