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We analyze the stability of scalarized charged black holes in theEinstein-Maxwell-Scalar (EMS) theory with quadratic coupling. These black holesare labelled by the number of $n=0,1,2,\cdots$, where $n=0$ is called thefundamental black hole and $n=1,2,\cdots$ denote the $n$-excited black holes.We show that the $n=0$ black hole is stable against full perturbations, whereasthe $n=1,2$ excited black holes are unstable against the $s(l=0)$-mode scalarperturbation. This is consistent with the EMS theory with exponential coupling,but it contrasts to the $n=0$ scalarized black hole in theEinstein-Gauss-Bonnet-Scalar theory with quadratic coupling. This implies thatthe endpoint of unstable Reissner-Nordstr\"{o}m black holes with $\alpha>8.019$is the $n=0$ black hole with the same $q$. Furthermore, we study the scalarizedcharged black holes in the EMS theory with scalar mass $m^2_\phi=\alpha/\beta$.

Stability of scalarized charged black holes in the Einstein-Maxwell-Scalar theory