Butterfly pivot is a large-travel rotational flexure pivot, which can provide elastic support for the rotational shaft in several ten degrees. Rotational precision is of great important for its application. Because of the complex structure, rotational precision is always taken with Finite Element Method (FEM), which is not suitable for design and optimize parametrically. The structure property of the butterfly pivot is analyzed before the precision analysis. Four-Blade Isosceles-Trapezoid Element is present as the basic structure unit of the Butterfly Pivot. And then, Rotational precision of the Four-blade Isosceles-Trapezoid unit is calculated and analyzed. The Self-Compensation performance of the butterfly Pivot is also studied. Work in this thesis can validate the high rotational precision of the butterfly pivot.