Compliant pivots are widely used in mechanical systems to provide accurate and repeatable rotations. However, the significant axial drift and low radial stiffness during the rotation of compliant pivots pose great challenges in the design and control of compliant pivot-based mechanisms. To mitigate these difficulties, this paper proposes a novel compliant pivot with nearly zero axial drift and high radial stiffness based on the rigid-body replacement method and symmetric arrangement. By designing a series of symmetric rigid linkages with one degree of freedom and substituting the rigid joints in them with compliant elements, several compliant building blocks are obtained. When arranging these building blocks in a circle, compliant pivots with zeros axial drift are obtained. By discussing the source of compliance in the radial direction, a pivot with high radial stiffness is obtained. The modeling of the pivot using a chained beam constraint model and a nonlinear finite element model demonstrates the kinetostatic properties of the pivot.