The paper considers the property of frequency-independent two-terminal networks (FITTN) formed by two parallel branches, each of which contains a single resistor and a dissipative two-terminal network with heterogeneous reactive elements. This property implies that after the transient process the frequency-independent two-terminal network has the constant resistance to the electric current in the case of the influence of the next feeding pulse signal with tension change as long as its duration under the law of exponential functions of time when fulfilling only a certain part of conditions of frequency independence (CFI). When fulfilling all conditions of frequency independence, FITTN has the constant resistance to the electric current at any forms of the feeding tension, and also during the transient process. The analysis of a special option of the frequency-independent two-terminal network uses the way which relieves the need to solve algebraic equations and hereby simplifies identical transformations. The article describes the use of FITTN in the pulse four-arm bridge circuits. Such bridges contain single resistors in three arms, and the fourth arm is formed by the frequency-independent two-terminal network. These bridge circuits allow grounding both multi-element two-terminal networks: the counterbalancing two-terminal network with variable adjustable parameters and the two-terminal network which is an object of measurement with the required parameters. This raises the possibility to exclude two components of the error: component due to the parasitic capacitance with respect to «ground» of the ungrounded multi-element two-terminal network and component due to the instability of this parasitic capacitance.