The single electron tunneling spectroscopy on superconductor Na$_{x}$CoO$_2$$cdot$ yH$_2$O and its starting compound Na$_{x}$CoO$_2$ has been studied with point-contact method. The spectra of Na$_{x}$CoO$_2$ have two types of distinct shapes at different random locations, this is attributed to the non-uniformly distributed sodium escaped from the inner part of the sample. While all the measured spectra of the superconducting samples Na$_{x}$CoO$_2$$cdot$ yH$_2$O have a good spatial reproducibility, and show a remarkable zero bias conductance depression appearing below an onset temperature which associates very well with the resistance upturn at around 45 K. The latter behavior resembles in some way the pseudogap feature in high-T$_c$ cuprate uperconductors.
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