  In this paper, we show how the two-particle Green function (2PGF) can be
obtained within the framework of the Dual Fermion approach. This facilitates
the calculation of the susceptibility in strongly correlated systems where
long-ranged non-local correlations cannot be neglected. We formulate the
Bethe-Salpeter equations for the full vertex in the particle-particle and
particle-hole channels and introduce an approximation for practical
calculations. The scheme is applied to the two-dimensional Hubbard model at
half filling. The spin-spin susceptibility is found to strongly increase for
the wavevector $\vc{q}=(\pi,\pi)$, indicating the antiferromagnetic
instability. We find a suppression of the critical temperature compared to the
mean-field result due to the incorporation of the non-local spin-fluctuations.
