  The $1^1D_2 (c\bar c)$ state is the ground state of spin-singlet D-wave
charmonia. Although it has not been found yet, the experimental data accumulate
rapidly. This charmonium attracts more and more attention, especially when the
BaBar Collaboration finds that the X(3872) particle has negative parity. In
this paper we calculate the double-gamma and double-gluon annihilation
processes of $^1D_2$ charmonia and bottomonia by using the instantaneous
Bethe-Salpeter method. We find the relativistic corrections make the decay
widths of $1^1D_2 (c\bar c)$ 2$\sim$5 times smaller than the non-relativistic
results. If this state is below the $D^0{D^{0}}^\ast$ threshold, we can use the
sum of annihilation widths and EM transition widths to estimate the total decay
width. Our result for $1{^1D_2} (c\bar c)$ with $m=3820$ GeV is $\Gamma= 432$
keV. The dominant decay channel $1^1D_2 (c\bar c)\to h_c \gamma$, whose
branching ratio is about 90%, can be used to discover this state.
