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A Light Emitting Diodes(LED) lighting is increasingly used because of its low power consumption and long lifetime. Of many power converters, a flyback converter is applied for the LED lightings and has some electrolytic capacitors for stabilizing the output voltage. But the expected life span of the electrolytic capacitors is much shorter than that of the LED elements. It makes the lifetime of the power converter with electrolytic capacitors for the LED lightings shorter than the LED elements. This paper represents the possibilities of eliminating electrolytic capacitors on the flyback converter. Also a revised version of the flyback converter is proposed. To verify the performance of the proposed converter, simulations were carried out.