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We investigate scalarized charged black holes in the Einstein-Maxwell-Scalartheory with two U(1) fields inspired by the $N=4$ supergravity. From the onsetof the spontaneous scalarization (tachyonic instability ofReissner-Nordstr\"{o}m black hole), these black holes are classified by thenumber of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental black holeand $n=1,2,\cdots$ denote the $n$-excited black holes. Adopting radialperturbations, we show that the $n=0$ black hole is stable against the$s(l=0)$-mode scalar perturbation, whereas the $n=1,2$ excited black holes areunstable. This implies that the $n=0$ black hole is considered as an endpointof the Reissner-Nordstr\"{o}m black hole.

Scalarized charged black holes in the Einstein-Maxwell-Scalar theory with two U(1) fields