  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
($3\leftrightarrow3$) qubit bidirectional quantum teleportation of a special
three-qubit entangled state. The novelty of our scheme lies in its
generalization for ($N\leftrightarrow N$) 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.
