  In this paper, we consider the following nonlinear Schr\"odinger equation
with derivative:
  \begin{align*}
  i\partial_tu+\partial_{xx}u+i|u|^{2}\partial_xu+b|u|^4u=0, \quad (t,x) \in
\mathbb{R}\times\mathbb{R}, \quad b\geq 0.
  \end{align*}
  For the case $b=0$, the original DNLS, Kwon and Wu \cite{KwonWu2018} proved
the conditional orbital stability of degenerate solitons including scaling,
phase rotation, and spatial translation with a non-smallness condition,
$\|u(t)\|_{L^6}^6> \sqrt{\delta}$. In this paper, we remove this condition for
the non-positive initial energy and momentum, and we extend the stability
result for $b\geq0$.
