  We prove that, for $\kappa\le 4$, backward chordal SLE$_\kappa$ admits
backward chordal SLE$_\kappa(-4,-4)$ decomposition for the capacity
parametrization.
  This means that, for any bounded measurable subset $U\subset Q_4:={\mathbb
R}_+\times{\mathbb R}_-$, if we integrate the laws of extended backward chordal
SLE$_\kappa(-4,-4)$ with different pairs of force points $(x,y)$ against some
suitable density function $G(x,y)$ restricted to $U$, then we get a measure,
which is absolutely continuous with respect to the law of backward chordal
SLE$_\kappa$, and the Radon-Nikodym derivative is a constant depending on
$\kappa$ times the capacity time that the generated welding curve $t\mapsto
(d_t,c_t)$ spends in $U$, where $d_t>0>c_t$ are the pair of points that are
swallowed by the process at time $t$. For the forward SLE curve, a similar
analysis has been done for SLE in the natural parametrization ([1] $\kappa \leq
4$, [10] $\kappa <8$), and for the capacity parametrization ([10] $\kappa <
\infty$).
