A derivation of the conservation laws for electromagnetic fields in vacuum which result from the invariance of Maxwell's equations under the conformal group is given. The arguments presented are easier to follow than those given by Bessel-Hagen in 1921, when the original investigation of these conservation laws was made. It is shown in this paper that four of the fifteen conservation laws can be derived from the remaining eleven. Only one of these eleven remains without physical interpretation. This particular conservation law is of some interest today in high-energy physics.