Abstract: The flexure hinge will produces a corresponding small elastic deformation when a force/torque is applied. Compliance performance can quantitatively describe the relation of the load and deformation, which influences the motion precision and the whole performance. The design of the flexure hinge is usually based on the complicated numerical integration and finite element method to calculate its performance index at present. A novel flexure hinge is presented in the paper. The compliance formulas of the novel flexure hinge are derived based on the elastic theory and calculus theory, which can instruct the design of the flexure hinge. The deformation formulas on the point along the central axis are reasoned strictly, the exact design and calculation of the flexure hinge is implemented. Those two consistent results prove the correctness of compliance formulas using software ANSYS.