  We study the manifestation of the $\Delta^{++}-\Delta^-$ component of the
deuteron wave function in the exclusive reaction $\bar p d \to \pi^- \pi^-
\Delta^{++}$. Due to the large binding energy the internal motion in the
$\Delta-\Delta$ system is relativistic. We take this into account within the
light-cone (LC) wave function formalism and, indeed, found large differences
between calculations based on the LC and non-relativistic (NR) wave functions.
We demonstrate, that the consistent LC treatment of the $\Delta-\Delta$ system
plays the key role in the separation of the signal and background. Within the
LC approach, the characteristic shape of the momentum distribution of the
$\Delta-\Delta$ bound system predicted by the meson-exchange model is well
visible on the background of usual annihilations at beam momenta between 10 and
15 GeV/c.
