Polarization and interfacial tension measurements at an electrolyte dropping electrode or a sessile electrolyte drop are used to investigate the instability of the interface between the aqueous solution of LiCl and the organic solvent containing a mixture of the electrolytes composed of the non-adsorbing ions, here tetrabutylammonium tetraphenylborate (TBATPB) and bis(triphenylphosphoranylidene) ammonium tetrakis (pentafluorophenyl)borate (BATB). The instability is manifested by a substantial current enhancement and decrease of the interfacial tension accompanied by the vigorous mechanical oscillations of the drop. In contrast, no instability is observed when the organic solvent phase contains TBATPB or BATB alone. It is proposed that the hydrodynamic instability has the origin in the small faradaic current associated with the trace ion transfer, and that the initiating impulse is generated by the perturbation of the stratified distribution of the ions with the significantly different sizes (e.g., TBA+ and BA+) on the organic side of the interface. Effects of the potential and the electrolyte concentration on the current enhancement and the interfacial tension reduction are explained by the kinematic theory that has been established by Aogaki et al. (Electrochim. Acta 23 (1978) 867).