We propose a new mechanism for paramagnetically catalyzed ortho-para conversion in molecular hydrogen. In this mechanism, a (3) Sigma(u)(+) excited-state character of H-2 is mixed into the ground state of a collisional complex, inducing spin-uncoupling and removal of antisymmetrization of the parts of the wave function localized to the hydrogen nuclei. This induces an effective Fermi contact hyperfine interaction between the ortho and para states. Using the collision complex H-2 + O-2 as model system, we show that the proposed mechanism is more than 2 orders of magnitude stronger than the traditional inhomogeneous magnetic field model.