  A recent paper (Phys. Rev. A \textbf{86}, 034305 (2012)) proposed an
entanglement concentration protocol (ECP) for distilling one pair of maximally
entangled multi-photon Greenberger-Horne-Zeilinger (GHZ) state from two pairs
of less-entangled multi-photon states with the photonic Faraday rotation. In
this paper, we put forward an improved ECP for arbitrary less-entangled
multi-photon GHZ state. In the ECP, we only require one pair of less-entangled
multi-photon state and one auxiliary photon, and the whole concentration
process only requires local operations. Moreover, our ECP can be used
repeatedly to further concentrate the less-entangled multi-photon state and
obtain a higher success probability. If consider the practical operation and
imperfect detection, our protocol is more efficient. This ECP may be useful in
current quantum information processing.
