Abstract. The conformal space M was introduced by Dirac in 1936. It is an algebraic manifold with a spin structure and possesses naturally an invariant Lorentz metric. By carefully studying the birational transformations of M, we obtain explicitly the transition functions of the spin bundle over M. Since the transition functions are closely related to the propagation in physics, we get a kind of solutions of the Dirac equation by integrals constructed from the propagation. Moreover, we prove that the invariant Lorentz metric together with one of such solutions satisfies the Einstein-Dirac combine equation.