It can be said that Maxwell's equations are one of the well-known equations of Physics. Despite the fact that this equations are more than hundred years old (1865), they still are the cornerstone of electrodynamics. Although they have several notations in the literature, this paper gives new representational method that based on dual quaternions. We have aimed the reformulation of classical electrodynamics. Therefore new dual quaternionic equations related with electromagnetism are derived.