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In this paper, we develop the modulation analysis, the perturbation argumentand the Virial identity similar as those in \cite{MartelM:Instab:gKdV} to showthe orbital instability of the solitary waves $\Q\sts{x-ct}\e^{\i\omega t}$ ofthe generalized derivative nonlinear Schr\"odinger equation (gDNLS) in thedegenerate case $c=2z_0\sqrt{\omega}$, where $z_0=z_0\sts{\sigma} $ is theunique zero point of $F\sts{z;~\sigma}$ in $\sts{-1, ~ 1}$. The new ingredientsin the proof are the refined modulation decomposition of the solution near $\Q$according to the spectrum property of the linearized operator $\Scal_{\omega,c}"\sts{\Q}$ and the refined construction of the Virial identity in thedegenerate case. Our argument is qualitative, and we improve the result in\cite{Fukaya2017}.

Instability of the solitary waves for the generalized derivative nonlinear Schr\"odinger equation in the degenerate case