Functionally relevant transitions between native conformations of a protein can be complex, involving, for example, the reorganization of parts of the backbone fold, and may occur via a multitude of pathways. Such transitions can be characterized by a transition network (TN), in which the experimentally determined end state structures are connected by a dense network of subtransitions via low-energy intermediates. We show here how the computation of a TN can be achieved for a complex protein transition. First, an efficient hierarchical procedure is used to uniformly sample the conformational subspace relevant to the transition. Then, the best path which connects the end states is determined as well as the rate-limiting ridge on the energy surface which separates them. Graph-theoretical algorithms permit this to be achived by computing the barriers of only a small number out of the many subtransitions in the TN. These barriers are computed using the Conjugate Peak Refinement method. The approach is illustrated on the conformational switch of Ras p21. The best and the 12 next-best transition pathways, having rate-limiting barriers within a range of 10 kcal/mol, were identified. Two main energy ridges, which respectively involve rearrangements of the switch I and switch II loops, show that switch I must rearrange by threading Tyr32 underneath the protein backbone before the rate-limiting switch II rearrangement can occur, while the details of the switch II rearrangement differ significantly among the low-energy pathways.