In five-axis machining, stability of the machining process is determined not only by the combination of depth of cut and spindle speed but also the cutter postures (orientations). In this article, we propose to construct posture stability graphs to guide the selection of cutter postures during tool-path generation. Posture stability graph provides a partitioning of the allowable range of cutter postures, dividing it into stable and chatter zones. Using postures only from the stable zone, we can achieve chatter avoidance without the trouble of tuning other process parameters like spindle speed. Posture stability graphs are constructed by identifying the cutter orientations that would render the machining system borderline stable under the given machining conditions. These postures would make the boundaries between stable and unstable zones on the posture stability graph. Such a process is achieved by modelling the machining system as a 2-degrees-of-freedom spring-mass-damper system and applying the full-discretization method for chatter identification. Many experiments have been carried out, based on which the effectiveness of the posture stability graph approach has been verified.