The three ab initio nonadiabatic coupling terms related to the three strongly coupled states of the C2H molecule, i.e., 2 (2)A('), 3 (2)A('), and 4 (2)A('), were studied applying the line integral technique [M. Baer, Chem. Phys. Lett. 35, 112 (1975)]. The following was verified: (1) Due to the close proximity of the conical intersections between these three states, two-state quantization cannot always be satisfied between two successive states. (2) It is shown that in those cases where the two-state quantization fails a three-state quantization is satisfied. This three-state quantization is achieved by applying the 3x3 nonadiabatic coupling matrix that contains the three relevant nonadiabatic coupling terms. The quantization is shown to be satisfied along four different contours (in positions and sizes) surrounding the relevant conical intersections.