The conical intersection (CI) between the 2(2)A' and 3(2)A' electronic states of C2H occurring at the C-2v-symmetric geometry has been characterized by line integral calculations using ab initio nonadiabatic matrix coupling elements. The calculations confirmed that when a path surrounds this CI and does not approach, too closely, CIs formed by adjacent states, the line integral produces for the topological phase, the expected pi -value. Increasing the radius of the circle was accompanied by a decrease in the topological phase indicating on the existence of other CIs in the vicinity of the present one.