  Iksanov and Pilipenko (2023) defined a skew stable L\'{e}vy process as a
scaling limit of a sequence of perturbed at $0$ symmetric stable L\'{e}vy
processes (continuous-time processes). Here, we provide a simpler construction
of the skew stable L\'{e}vy process as a scaling limit of a sequence of
perturbed at $0$ standard random walks (random sequences).
