  We conducted multi-epoch VLBI observations to search for astrometric reflex
motion caused by a sub-stellar companion of the M8.5 dwarf TVLM 513-46546. The
observations yield an absolute parallax corresponding to a distance of
10.762+/-0.027 pc and a proper motion of 78.09+/-0.17 mas/yr. From the absence
of significant residual motion, we place an upper limit to any reflex motion
caused by a companion, extending the parameter space covered by previous
near-infrared direct-imaging searches. By covering different orbital periods,
the data exclude a phase-space of companion masses and orbital periods ranging
from 3.8 Mjup with an orbital radius of ~0.05 AU (orbital period of 16 days) to
0.3 Mjup with an orbital radius of ~0.7 AU (orbital period of 710 days).
