  The new particle Z(3930) found by the Belle and BaBar Collaborations through
the $\gamma\gamma\rightarrow D\bar D$ process is identified to be the
$\chi_{c2}(2P)$ state. Since the mass of this particle is above the $D\bar
D^{(\ast)}$ threshold, the OZI-allowed two-body strong decays are the main
decay modes. In this paper, these strong decay modes are studied with two
methods. One is the instantaneous Bethe-Salpeter method within Mandelstam
formalism. The other is the combination of the $^3P_0$ model and the former
formalism. The total decay widths are 26.3 and 27.3 MeV for the methods with or
without the $^3P_0$ vertex, respectively. The ratio of $\Gamma_{D\bar D}$ over
$\Gamma_{D\bar D^\ast}$ which changes along with the mass of the initial meson
is also presented.
