We conducted multi-epoch very long baseline interferometry observations to search for astrometric reflex motion that would be 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–1. The averaged flux density per epoch varies by a factor of at least three. From the absence of significant residual motion, we place an upper limit on any reflex motion caused by a companion, extending the parameter space covered by previous near-infrared direct-imaging searches. The data exclude a phase space of companion masses and orbital periods ranging from 3.8 M Jup with an orbital radius of ~0.05 AU (and an orbital period of 16 days) to 0.3 M Jup with an orbital radius of ~0.7 AU (and an orbital period of 710 days).
