In the precision point synthesis of mechanisms, it is usually required to solve a system of polynomial equations. With the aid of efficient algorithms such as elimination, it is possible to obtain all the solutions of the equations in the complex domain. But among these solutions only real values can be used fur real mechanisms, while imaginary ones are liable to be discarded. In this article, a method is presented, which leads the imaginary solutions to real domain permitting slight alteration of prescribed positions and eventually increases the number of feasible mechanisms satisfying the desired motion approximately. Two synthesis problems of planar 4-bar path generation and spatial 7-bar motion generation are given to verify the proposed method.