Biped climbing robots are considered good assistants and (or) substitutes for human workers carrying out high-rise truss-associated routine tasks. Flexible locomotion on three-dimensional complex trusses is a fundamental skill for these robots. In particular, the capability to transit from one structural member to another is paramount for switching objects to be climbed upon. In this paper, we study member-to-member transition and its utility in global path searching for biped climbing robots. To compute operational regions for transition, hierarchical inspection of safety, reachability, and accessibility of grips is taken into account. A novel global path rapid determination approach is subsequently proposed based on the transition analysis. This scheme is efficient for finding feasible routes with respect to the overall structural environment, which also benefits the subsequent grip and motion planning. Simulations are conducted with Climbot, our self-developed biped climbing robot, to verify the efficiency of the presented method. Results show that our proposed method is able to accurately determine the operational region for transition within tens of milliseconds and can obtain global paths within seconds in general.