We will consider the Yamabe Problem on globally hyperbolic spatially compact Lorentzian manifolds (M,g) of dimension 4: Given a Lorentzian metric g on M, find a metric conformal to g with constant scalar curvature. This is equivalent to finding a smooth global solution to a certain semilinear wave equation. In the case of a standard static spacetime, it is well known that for a given negative constant scalar curvature there does not exist a smooth global solution if f.e. the scalar curvature of (M,g) is positive. We want to prove that in this case there still exists a global H^2-solution of this semilinear equation.