Reconfigurable composite joints (RCJs) are essential elements in the design of reconfigurable mechanisms. One significant trend is to synthesize RCJs with pre-specified motion properties. This paper focuses on the general synthesis method for the design of RCJs based on motion decomposition and reconstruction (MDR). The overall concept of MDR targeting the design of RCJs is first introduced. Then, the concept and its application are described, including six steps: (i) determination of the main chain (MC); (ii) motion modeling of the MC; (iii) analysis and decomposition of the total motion of the MC; (iv) reconstruction of the chains with different submotions by means of auxiliary chains (ACs); (v) determination of the pertinent adjustable chain, and assembly of the MC, ACs, and the adjustable chain; and (vi) layout of the actuation scheme. Subsequently, three kinds of RCJs with different main chains are generated systematically by means of the concepts proposed herein. Finally, one reconfigurable parallel-kinematics machine (PKM) with one proposed RCJ in a limb is used as an example, which offers applications in the design of reconfigurable mechanisms. The proposed concept, MDR, is not only suitable for type synthesis of simple kinematic chains, but also potentially applicable to reconfigurable kinematic chains.