  The SU(3)-flavor violating decay $J/\psi\to\Xi(1530)^{-}\bar\Xi^{+}+c.c.$ is
studied using $(1310.6\pm7.0)\times 10^{6} ~J/\psi$ events collected with the
BESIII detector at BEPCII and the branching fraction is measured to be
  ${\cal{B}}(J/\psi\to\Xi(1530)^{-}\bar\Xi^{+}+c.c.)=(3.17\pm0.02_{\rm
stat.}\pm0.08_{\rm syst.})\times10^{-4}$. This is consistent with previous
measurements with an improved precision. The angular parameter for this decay
is measured for the first time and is found to be $\alpha=-0.21\pm0.04_{\rm
stat.}\pm0.06_{\rm syst.}$. In addition, we report evidence for the radiative
decay $\Xi(1530)^{-}\to\gamma\Xi^- $ with a significance of 3.9$\sigma$,
including the systematic uncertainties. The 90\% confidence level upper limit
on the branching fraction is determined to be
$\mathcal{B}(\Xi(1530)^{-}\to\gamma\Xi^- )\leq3.7$\%.
