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A new quench monitoring system by using the Poynting Vector method was proposed. This new system can indirectly detect normal transitions which are suddenly induced during an operation of superconducting coils. In this system, the superconducting coil is surrounded by the thin metallic cylinder composed of several pieces, where the cylinder is electrically insulated from the coil; potential leads to measure local electric fields are directly attached to this cylinder surface and pickup coils to measure local magnetic fields are put on the surface. The Poynting vector distribution around the coil can be obtained by using many sets of both the potential lead and the pickup coil. Since sudden changes of energy flow profiles around the superconducting coil are induced in the event of local normal transitions of the coil winding, such an event of coils can be detected by the change of the Poynting vector. This system has no risk of the destructive voltage breakdown which may happen in case of the existing balance voltage method, because there is no need of direct contacts on the coil windings. In addition, this method is expected to be higher reliability and sensitivity than the acoustic emission method. A demonstration test was carried out of monitoring the quench for the Bi-2223 coil partially immersed in liquid nitrogen, and a sign of normal transitions before the quench was successfully detected by this method. [ABSTRACT FROM AUTHOR]