  The pearling instability of bilayer surfactant tubes was recently observed
during the collapse of fluid monolayers of binary mixtures of DMPC$-$POPG and
DPPC$-$POPG surfactants. We suggested it has the same physics as the well-known
Raleigh instability under the action of the bilayer surface tension whose
magnitude is dictated by the electrostatic interaction between charged
surfactants. In this paper, we calculate the relaxation of charge molecules
during the deformation of the tubes into pearling structure. We find the
functional dependence of the relaxation energy on the screening length
$\kappa^{-1}$ explicitly. Relaxation effect lowers the cost of bending a tube
into pearls making the cylindrical tube even more unstable. It is known that
for weak screening case where the tube radius is smaller than the screening
length of the solution, this relaxation effect is important. However, for the
case of strong screening it is negligible. For the experiments mentioned, the
situation is marginal. In this case, we show this relaxation effect remains
small. It gives less than 20% contribution to the total electrostatic energy.
