In this paper, a new reconfigurable 6R linkage is obtained by combining two identical equilateral Bennett linkages arranged in a plane-symmetric manner, and a detailed kinematic analysis is conducted which shows that there are six distinct motion modes and three topological structures of the derived mechanism without changing the types of kinematic joints. Explicit relationships among the kinematic variables are obtained with D–H method and various modes are discussed in detail. Bifurcation points are derived and the reconfigurations are analyzed. The result shows that the mechanism has six motion modes which contain a special case of a plane-symmetric 6R mode and a special case of a two-fold symmetric 6R mode, an X-shaped motion mode, and two V-shaped motion modes. A physical prototype is fabricated to verify the derivation and it shows that the mechanism can transform among all the motion modes without the need of reassembling.