It is stated in nearly all textbooks that the electric and magnetic fields of any plane electromagnetic wave in free space are always in phase,no matter whether the textbooks are in Chinese or in English,whether they are College Physics,Electromagnetics,or Electrodynamics. Based on Maxwell’s equations,we prove in this paper that the above statement is actually not always correct. In general case,we can only state that the electric and magnetic fields of a plane electromagnetic wave in free space are in step,which can be in phase or out of phase,depending on the choice of coordinate systems.