We synthesized powder samples of Na$_{x}$CoO$_{2}cdot y$H$_{2}$O changing the volume of the water in the hydration process, then investigated their superconducting properties,. It was proved that the volume of water is one of key parameters to obtain a single phase of Na$_{x}$CoO$_{2}cdot y$H$_{2}$O with good superconducting properties. The transition temperature, $T_{c}$, of the sample changed gradually while it was stored in the atmosphere of 70% humidity. Superconducting behavior under high magnetic field was very sensitive to $T_{c}$. $H_{c2}$ of a high quality sample with high $T_{c}$ seemed very high.
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