If any normal subgroup of a group G is Φ-invariant for some automorphism Φ of G, then Φ is called a normal au-tomorphism. Each inner automorphism of a group is normal, but the converse is not true in the general case. We prove that any normal automorphism of the free Burnside group B(m, 3) of period 3 is inner for each rank m ≥ 3.