  We study topological properties of phase transition points of two
topologically non-trivial $\mathbb{Z}_2$ classes (D and DIII) in one dimension
by assigning a Berry phase defined on closed circles around the gap closing
points in the parameter space of momentum and a transition driving parameter.
While the topological property of the $\mathbb{Z}_2$ system is generally
characterized by a $\mathbb{Z}_2$ topological invariant, we identify that it
has a correspondence to the quantized Berry phase protected by the
particle-hole symmetry, and then give a proper definition of Berry phase to the
phase transition point. By applying our scheme to some specific models of class
D and DIII, we demonstrate that the topological phase transition can be well
characterized by the Berry phase of the transition point, which reflects the
change of Berry phases of topologically different phases across the phase
transition point.
