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In this work, we shall demonstrate that timeaveraged stored energy density (TASED) of a circularly polarized wave is equal to zero, in addition, TASEDs of both circularly and linearly polarized waves do not directly relate to their time-averaged Poynting vector (TAPV), respectively, which indicates that the usual definition of energy flow velocity needs to be reconsidered. Noting that energy U of electromagnetic wave (photon) obtained from relativistic energy-momentum relation corresponds to transport of electromagnetic energy, combining expressions of both TAPV and time-averaged electromagnetic wave momentum density, a new definition of energy flow velocity is proposed by applying energy U instead of TASED. Furthermore, we shall show from the new definition that a rational energy flow velocity of electromagnetic wave traveling in a material medium is obtained by adopting Minkowski electromagnetic wave momentum density, which may provide a new way to further discuss the long-standing Abraham-Minkowski controversy.