Parametric design is the core of the current CAD technology. The way tomanage the constraints conveniently and efficiently is required by the procedures to modeland solve the geometric constraint system which is the base of parametric design. A newmethod called as MRA(maximal reduction algorithm) is presented in this paper. It owesto the application about analysis of degree of freedom, graph theory and sparse matrix theory. The MRA is very effective for geometric constraint consistency checking, maximaldecomposition of geometric constraint system and constraint management. It is worth thatthe MRA express the serial, parallel and coupling mechanism of constraint propagationwith reducing tree.