  Magnetic properties of the novel layered superconductor,
Na$_{0.35}$CoO$_{2}$$\cdot$1.3H$_{2}$O have been investigated. From the
temperature dependence and field dependence of the magnetization, the
superconducting transition temperature, as well as upper- and lower-critical
fields have been estimated to be $T_{C}=4.6$ K, $H_{C2}(0)=61.0$ T and
$H_{C1}(0)=28.1$ Oe. These values give quite unusual phenomenological
parameters, \textit{i.e.}, coherent length, penetration depth and
Ginzburg-Landau parameter of $\xi=2.32$ nm, $\lambda=5.68\times 10^{3}$ \AA\
and $\kappa\equiv\lambda/\xi=244$, suggesting an unconventional nature of
superconductivity. Normal-state magnetic susceptibility shows an upturn below
130 K, which is confirmed to be inherent by high-field magnetization data. The
upturn may have relevance to the mechanism of the superconductivity.
