  An algebraic proof of the nonrenormalization theorem for the perturbative
beta function of the coupling constant of N=2 Super Yang-Mills theory is
provided. The proof relies on a fundamental relationship between the N=2
Yang-Mills action and the local gauge invariant polynomial Tr phi^2, phi(x)
being the scalar field of the N=2 vector gauge multiplet. The
nonrenormalization theorem for the beta function follows from the vanishing of
the anomalous dimension of Tr phi^2.
