<p>Chatter stability analysis can be employed to determine the stability behavior of a milling process because the regenerative chatter can reduce the machining quality and limit the efficiency of productivity. Hence, precise and efficient construction of stability lobe diagrams (SLDs) is very helpful for the milling processes in maintaining a chatter-free system. In this study, using the analytical solution of the free vibration, a precise and efficient updated third-order full-discretization method (PE3rdFDM) is proposed to create the SLDs. In each time interval being discretized, the state term is defined approximately by the third-order Hermite interpolation polynomial, and the derivative values needed to conduct the Hermite interpolation are provided by the original DDEs. To handle the time-delay term, the original integral of the equation obtained by directly integrating the DDE is divided into two parts. For the part with the time delay term, the updated numerical integration formula is used for approximation. Moreover, a precise integration (PI) algorithm is utilized to calculate the matrix exponentials efficiently and accurately. In addition, a transition matrix is established to determine the SLDs. The performance evaluation performed by the comparison demonstrates that the proposed method outperforms the other existing methods. A demonstrative example is presented to illustrate the usage of the proposed method. Although a stability prediction tool for milling processes is a particular application presented here, the proposed method can be applied to turning, boring, and drilling processes in general.</p>