  Recently, Ri-Gui Zhou et al. [Int. J. Theor. Phys. 59, 166-172 (2020)]
proposed a scheme for bidirectional quantum teleportation of two-two and
two-three qubit states by utilizing a six-qubit entangled state as a quantum
channel. It is observed that the intrinsic efficiency calculated by Zhou et al.
is not correct. In this improved scheme, we show that bidirectional
teleportation of two-two and two-three qubit quantum states can be done by
using optimized quantum resource and less consumption of classical resource. We
also calculate the intrinsic efficiency of our improved scheme which is much
better than the Zhou's scheme. Additionally, we also discuss about the security
of the protocol.
