  Under the framework of the Bethe-Salpeter (B.S.) wave functions and the
Mandelstam formalism as well, to make ``instantaneous approximation'' to a
transition matrix element (a current operator sandwiched between two
bound-states of double heavy quarks) is described. By taking the typical
concerned decays as examples, such as $B_c$ meson decaying to $J/\psi + (\bar l
\nu)$, the advantages of the approach and its limitations are illustrated.
Finally, potential applications to various processes for possible double heavy
flavoured systems, such as those of $(Q' \bar Q)$ and $(Q' Q)$ ($m_Q, m_{Q'}\gg
\Lambda_{QCD}$), are discussed.
