  The instantaneous formulations for the relativistic Bethe-Salpeter (BS) and
the radiative transitions between the bound-states are achieved if the BS
kernel is instantaneous. It is shown that the original Salpeter instantaneous
equation set up on the BS equation with an instantaneous kernel should be
extended to involve the `small (negative energy) component' of the BS wave
functions. As a precise example of the extension for the bound states with one
kind of quantum number, the way to reduce the novel extended instantaneous
equation is presented. How to guarantee the gauge invariance for the radiative
transitions which is formulated in terms of BS wave functions, especially,
which is formulated in the instantaneous formulation, is shown. It is also
shown that to `guarantee' the gauge invariance for the radiative transitions in
instantaneous formulation, the novel instantaneous equation for the bound
states plays a very important role. Prospects on the applications and
consequences of the obtained instantaneous formulations are outlined.
