We have first used the aquesous KMnO4 solution to de-intercate and oxidize γ-phase of Na0.7CoO2 and successfully form the superconducting phase cobalt oxyhydrates with onset Tc = 3.4 - 4.6 K. It is found that the phase stability of superconducting cobalt oxyhydrate phase is unstable with respect to the ambient humidity and vacuum but is reversible in terms of phase crystallinity. According to the thermogravimetric analyses (TGA) and x-ray diffraction (XRD) patterns, two relatively stable phases can be identified at relatively low temperatures as a result of dehydration of the cobalt oxyhydrate. In this paper, the phase stability of NaxCoO2.yH2O obtained using Br2 in acetonitrile solution is also discussed.