  In the quark-diagram scheme, we study the charmed baryon decays of ${\bf
B}_c\to {\bf B}^* M$, where ${\bf B}_c$ is $\Lambda_c^+$ or $\Xi_c^{+(0)}$,
together with ${\bf B}^*$ ($M$) the decuplet baryon (pseudoscalar meson). It is
found that only two $W$-exchange processes are allowed to contribute to ${\bf
B}_c\to {\bf B}^* M$. Particularly, we predict ${\cal B}(\Lambda_c^+ \to
\Sigma^{*0(+)} \pi^{+(0)})=(2.8\pm 0.4)\times 10^{-3}$, which respects the
isospin symmetry. Besides, we take into account the $SU(3)$ flavor symmetry
breaking, in order to explain the observation of ${\cal B}(\Lambda_c^+\to
\Sigma^{*+}\eta)$. For the decays involving $\Delta^{++}(uuu)$, we predict
${\cal B}(\Lambda_c^+\to \Delta^{++} \pi^-,\Xi_c^+ \to \Delta^{++} K^-)
=(7.0\pm 1.4,13.5\pm 2.7)\times 10^{-4}$ as the largest branching fractions in
the singly Cabibbo-suppressed $\Lambda_c^+,\Xi_c^+\to{\bf B}^*M$ decay
channels, respectively, which are accessible to the LHCb, BELLEII and BESIII
experiments.
