  We report the first observation of the Cabibbo-suppressed decays
$\Xi_c^0\rightarrow \Xi^- K^+$, $\Xi_c^0\ra\Lambda K^+ K^-$ and
$\Xi_c^0\rightarrow \Lambda \phi$, using a data sample of $711\,
\mathrm{fb}^{-1}$ collected at the $\Upsilon(4S)$ resonance with the Belle
detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We measure the
ratios of branching fractions to be $\frac{{\cal B}(\Xi_c^0\ra \Xi^-
K^+)}{{\cal B}(\Xi^0_c\ra\Xi^-\pi^+)}=(2.75\pm 0.51\pm 0.25)\times 10^{-2}$,
$\frac{{\cal B}(\Xi_c^0\ra\Lambda K^+ K^-)}{{\cal B}(\Xi_c^0\rightarrow\Xi^-
\pi^+)}=(2.86\pm 0.61\pm 0.24)\times 10^{-2}$ and $\frac{{\cal B}(\Xi_c^0\ra
\Lambda\phi)}{{\cal B}(\Xi^0_c\ra\Xi^-\pi^+)}=(3.43\pm 0.58\pm 0.32)\times
10^{-2}$, where the first uncertainty is statistical and the second is
systematic.
