Butterfly pivot is a large-travel rotational flexure pivot, which can provide elastic support for the rotational shaft in several ten degrees. Because of the complex structure, stiffness calculation of butterfly pivot is always completed by the method of Finite Element Analysis (FEA), which is not suitable for parameter design and optimization. The serial structure of four-blade isosceles-trapezoid (FBIT)is proposed to simplified the complex structure of the butterfly pivot. The FBIT is analyzed and the theoretical formula of stiffness calculation for rotation stiffness is derived in detail based on the essential theory of Mechanics of Materials. Design and optimization of rotation stiffness for each element can be achieved easily with the obtained the theoretical formula of rotation stiffness. The total rotation stiffness of the whole butterfly pivot is calculated and the rotation stiffness comparison between using the theoretical method and by the method of FEA is performed. The error between the theoretical rotation stiffness and the result of the FEA is less than 10%. It is acceptable and without any influence on the validity of the work and concept presented in this paper.