A noncombinatorial method for structural observability analysis is presented in this paper. The technique rearranges the process occurrence matrix to a specific block lower-triangular pattern by means of bigraphs and digraphs in two consecutive stages. The algorithmic core is constituted of a new node classification that leads to suitable maximum-matching decompositions even for structurally singular matrices. A three-step strategy for the identification and analysis of forbidden subsets was also designed to take into account the additional numeric constraints that guarantee further solvability of the final pattern. In contrast with other structural techniques, the proposed method treats complex nonlinear models in a remarkably efficient way. Its performance was compared with existing structural observability techniques for three industrial problems. The final results revealed that the direct method is extremely robust and efficient in computing times, becoming more efficacious as problems grow in size and complexity.