Obtained in this note are an elementary constructive proof and a strengthened form, based on the proof, of the following theorem on finitely dimensional central simple algebras. Let E/F be a finite Galois extension field over F,G=Gal E/F.Ifk is a normal Noether factor set, then c defined by c（ρ,σ,τ） =ρk,ρ,-1,σ,σ,-1,τ is a reduced Brauer factor set, and（E, G, k）≌E（E, c）. Conversely, if c is a reduced Brauer factor set, then k,σ,τ,=c（1,σ,στ） defines a normal Noether factor set, and B（E, c）≌（E, G, k）.