Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two quantum nodes. All bidirectional quantum teleportation protocols till now have achieved a maximum efficiency of 40%. Here, we propose a new scheme for symmetric bidirectional quantum teleportation using a six-qubit cluster state as the quantum channel, for symmetric (3 ↔ 3) qubit bidirectional quantum teleportation of a special three-qubit entangled state. The novelty of our scheme lies in its generalization for (N ↔ N ) qubit bidirectional quantum teleportation employing a 2N -qubit cluster state. The efficiency of the proposed protocol is remarkably increased to 50% which is highest till now. Interestingly, only GHZ-state measurements and four Toffoli-gate operations are necessary which is independent of the number (N ) of qubits to be teleported.