  It is believed that the quantum coherence itself cannot explain the very high
excitation energy transfer (EET) efficiency in the Fenna-Matthews-Olson (FMO)
complex. In this paper, we show that this is not the case if the inter-site
couplings take complex values. By phenomenologically introducing phases into
the inter-site couplings, we obtain the EET efficiency as high as 0.8972 in
contrast to 0.6781 with real inter-site couplings. Dependence of the excitation
energy transfer efficiency on the initial states is elaborated. Effects of
fluctuations in the site energies and inter-site couplings are also examined.
