The synthesis of four-bar mechanisms is a well-understood, classical design problem. The original systematic work in this field began in the late 1800s and continues to be an active area of research. Limitations to the classical theory of four-bar synthesis potentially limit its application to certain real-world problems by virtue of the small number of precision points and unspecified order. This paper presents a numerical technique for four-bar mechanism synthesis based on genetic algorithms that removes this limitation by relaxing the accuracy of the precision points.