This Note presents a kind of paired double parallelogram (DP) flexure mechanism clamped by a sinusoidal corrugated beam to solve the problem of underconstraint of its secondary stages. The results show that the proposed mechanism effectively constrains the undesired motions of the secondary stages without changing the stiffness and the first-order natural frequency in the working direction. The second- and third-order natural frequencies of the mechanism are increased by 9.2% and 30.8%, respectively, which can effectively improve the dynamic characteristics of the DP mechanism.