  This letter investigates the transport properties of MHD turbulence induced
by the magnetorotational instability at large Reynolds numbers Re when the
magnetic Prandtl number Pm is larger than unity. Three MHD simulations of the
magnetorotational instability (MRI) in the unstratified shearing box with zero
net flux are presented. These simulations are performed with the code Zeus and
consider the evolution of the rate of angular momentum transport as Re is
gradually increased from 3125 to 12500 while simultaneously keeping Pm=4. To
ensure that the small scale features of the flow are well resolved, the
resolution varies from 128 cells per disk scaleheight to 512 cells per
scaleheight. The latter constitutes the highest resolution of an MRI turbulence
simulation to date. The rate of angular momentum transport, measured using the
alpha parameter, depends only very weakly on the Reynolds number: alpha is
found to be about 0.007 with variations around this mean value bounded by 15%
in all simulations. There is no systematic evolution with Re. For the best
resolved model, the kinetic energy power spectrum tentatively displays a
power-law range with an exponent -3/2, while the magnetic energy is found to
shift to smaller and smaller scales as the magnetic Reynolds number increases.
A couple of different diagnostics both suggest a well-defined injection length
of a fraction of a scaleheight. The results presented in this letter are
consistent with the MRI being able to transport angular momentum efficiently at
large Reynolds numbers when Pm=4 in unstratified zero net flux shearing boxes.
