Magnetic energy harvesting extracts energy from magnetic fields generated from AC current, providing power for low-power devices. Previous research suggests the magnetic core operates in a slightly saturated state to obtain the maximum power output, but power transfer ceases once the core reaches full saturation. To address this limitation, a desaturation scheme is proposed, which employs an additional control voltage to maintain the magnetic core in its desaturated state, thereby generating multiple power transfer windows in each period and enhancing the harvested power via MEH. Furthermore, LTspice simulations and experiments are conducted to examine the effects of the load voltage and the number of power transfer windows on the amount of harvested power. The results demonstrate that the proposed desaturation scheme can significantly increase the harvested power of MEH systems by 200% compared to the scenario where the desaturation scheme is not utilized and the core reaches a state of hard saturation.