  An extended collinearly-improved Balitsky-Kovchegov evolution equation in the
target rapidity representation is derived by including the running coupling
corrections during the expansion of the "real" $S$-matrix. We find that the
running coupling brings important corrections to the evolution equation, as one
can see that there are extra contributions to the evolution kernel once the
running coupling is included. To identify the significance of the corrections,
we numerically solve the evolution equation with and without the running
coupling contributions during the $S$-matrix expansion. The numerical results
show that the scattering amplitude is largely suppressed by the running
coupling corrections, which indicate that one needs to consider the running
coupling contributions during the derivation of the non-linear evolution
equation in the target rapidity representation.
