  Kitaev chain model with nearest neighbor interaction U is solved exactly at
the symmetry point $\Delta=t$ and chemical potential $\mu=0$ in open boundary
condition. By applying two Jordan-Wigner transformations and a spin-rotation,
such a symmetric interacting model is mapped to a non-interacting fermion
model, which can be diagonalized exactly. The solutions include topologically
non-trivial phase at $|U|<t$ and topologically trivial phase at $|U|>t$. The
two phases are related by dualities. Quantum phase transitions in the model are
studied with the help of the exact solution.
