This article presents a novel method for the dimensional synthesis of Stephenson-II function generators without order, circuit, and branch defects. The explicit equations relating the generated output and specified variables of Stephenson-II function generators are derived by eliminating and transforming angular variables on two five-bar loops and by using the specified values of input and output variables. Then, the deviation between the generated and required angular positions of the output link of the synthesized mechanism is obtained for the objective function. Using the characteristics of order, circuits, branches, and the geometric features of dead-center configurations for Stephenson-II function generators, the constraint equations for avoiding these defects are proposed for the optimal synthesis of Stephenson-II function generators. The synthesized mechanisms are shown to be defect-free and satisfy all functional requirements. An example is given to demonstrate the feasibility of the proposed method.