  Weak radiative hyperon decays, important to test the strong interaction and
relevant in searches for beyond the standard model physics, have remained
puzzling both experimentally and theoretically for a long time. The recently
updated branching fraction and first measurement of the asymmetry parameter of
$\Lambda\to n\gamma$ by the BESIII Collaboration further exacerbate the issue,
as none of the existing predictions can describe the data. We show in this
letter that the covariant baryon chiral perturbation theory, with constraints
from the latest measurements of hyperon non-leptonic decays, can well describe
the BESIII data. The predicted branching fraction and asymmetry parameter for
$\Xi^-\to\Sigma^-\gamma$ are also in agreement with the experimental data. We
note that a more precise measurement of the asymmetry parameter, which is
related with that of $\Sigma^+\to p\gamma$, is crucial to test Hara's theorem.
We further predict the branching fraction and asymmetry parameter of
$\Sigma^0\to n\gamma$, whose future measurement can serve as a highly
nontrivial check on our understanding of weak radiative hyperon decay and on
the covariant baryon chiral perturbation theory.
