  PSR J1357$-$6429 is a young and energetic radio pulsar detected in X-rays and
$\gamma$-rays. It powers a compact pulsar wind nebula with a jet visible in
X-rays and a large scale plerion detected in X-ray and TeV ranges. Previous
multiwavelength studies suggested that the pulsar has a significant proper
motion of about 180 mas yr$^{-1}$ implying an extremely high transverse
velocity of about 2000 km s$^{-1}$. In order to verify that, we performed
radio-interferometric observations of PSR J1357$-$6429 with the the Australia
Telescope Compact Array (ATCA) in the 2.1 GHz band. We detected the pulsar with
a mean flux density of $212\pm5$ $\mu$Jy and obtained the most accurate pulsar
position, RA = 13:57:02.525(14) and Dec = $-$64:29:29.89(15). Using the new and
archival ATCA data, we did not find any proper motion and estimated its 90 per
cent upper limit $\mu < 106$ mas yr$^{-1}$. The pulsar shows a highly polarised
single pulse, as it was earlier observed at 1.4 GHz. Spectral analysis revealed
a shallow spectral index $\alpha_{\nu}$ = $0.5 \pm 0.1$. Based on our new radio
position of the pulsar, we disclaim its optical counterpart candidate reported
before.
