  We investigate the dissipation of magnetic flux in primordial star-forming
clouds throughout their collapse including the run-away collapse phase as well
as the accretion phase. We solve the energy equation and the non-equilibrium
chemical reactions in the collapsing gas, in order to obtain the radial
distribution of the ionized fraction during the collapse. As a result, we find
the ionized fraction is high enough for the magnetic field to couple with the
gas throughout the evolution of the cloud. This result suggests that the jet
formation from protostars as well as the activation of magneto-rotational
instability in the accretion disk are enabled in the presence of the
cosmological seed magnetic flux proposed by Langer et al.(2003).
