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One form of the five-element minimum-resistance bridge network consists of equal resistors in one pair of opposite side-arms of a bridge structure, equal inductors in the other pair of opposite side-arms, and a capacitor in the cross-arm. This gives a biquadratic impedance, since, by virtue of the equal impedances in opposite cross-arms, the bicubic impedance inherent in such a network automatically reduces to a biquadratic function. It is shown in this paper that, if such a network is generalized to the extent of having opposite elements in the bridge of unequal magnitude, but still of the same kind, the impedance will still reduce to a biquadratic function under certain conditions. These conditions are determined explicitly, together with formulas for the synthesis of such a network.