  We have observed two new decay modes of the charmed baryon $\Xi_c^+$ into
$\Sigma^+ K^-\pi^+$ and $\Sigma^+ \bar{K}^{*0}$ using data collected with the
CLEO II detector. We also present the first measurement of the branching
fraction for the previously observed decay mode $\Xi_c^+\to\Lambda
K^-\pi^+\pi^+$. The branching fractions for these three modes relative to
$\Xi_c^+\to\Xi^-\pi^+\pi^+$ are measured to be $1.18 \pm 0.26 \pm 0.17$, $0.92
\pm 0.27 \pm 0.14$, and $0.58 \pm 0.16 \pm 0.07$, respectively.
