Mathematically a 2Dconstrained design system can be modeled by m independent nonlinear equa－tions with n design variables and the design process can be viewed as a process ofsolving a geometric constraintsystem．Design decomposition is a highly effective way to improve a geometric constraint solver to make it effi－cient and robust．This paper reports a graph based decomposing approach and gives the correctness proof oftheapproach：（1）this approach can dealwith the decomposition ofstructurally under－constrained systems，（2）thisapproach can detect structurally over－constrained systems，（3）the approach can terminate within finite numberofsteps，and（4）the solving steps obtained through the decomposing approach are structurally consistent．