Abstract: A novel single axis flexure hinge named secant flexure hinge is presented. Based on the Castigliano’s second theorem, the closed-form equations are formulated for the compliance and precision of the rotation of the hinge by defining an intermediate parameter in the equations. And the stress levels of the hinge are also evaluated in terms of the compliances. Checked against finite element analysis, the results of the finite element analysis and the analytical ones are in good agreement. A unitary compliance-based analysis is performed by means of two-dimensional geometric parameters of the hinge, which provides important theoretical principles for engineering design of flexure hinges.