In the temperature (T)-ν Q3 phase diagram of Na x CoO 2 ⋅yH 2 O, there exist two superconducting regions of ν Q3 separated by the nonsuperconducting region, where ν Q3 is usually estimated from the peak position of the 59 Co-NQR spectra of the ±5/2↔ ±7/2 transition and well-approximated here as ν Q3~3 ν Q , ν Q being the interaction energy between the nuclear quadrupole moment and the electric field gradient. We have carried out measurements of the 59 Co-NMR Knight shift (K) for a single crystal in the higher-ν Q3 superconducting phase and found that K begins to decrease with decreasing T at T c for both magnetic field directions parallel and perpendicular to CoO 2 -planes. The result indicates together with the previous ones that the superconducting pairs are in the spin-singlet state in both phases, excluding the possibility of the spin-triplet superconductivity in this phase diagram. The superconductivity of this system spreads over the wide ν Q3 regions, but is suppressed in the narrow region located at the middle point of the region possibly due to charge instability. KEYWORDS: Na x CoO 2 ⋅yH 2 O, superconductivity, NMR, Knight shift, phase diagram Na 0.3 CoO 2 ⋅1.3H 2 O with the superconducting transition temperature T c of ∼4.5 K has the two-dimensional triangular lattice of Co atoms. 1) Due to this structural characteristic, not only this system and but also the mother system Na x CoO 2 have attracted much attention in relation to a possible geometrical frustration of the electron spins. 2) To identify the mechanism of the superconducting pairing, we have clarified various kinds of their physical properties: The T c value has been found to depend on the 59 Co nuclear quadrupole frequency ν Q , as summarized in the T−ν Q3 phase diagram shown in Fig. 1, ν Q3 (~3ν Q ) being the frequency corresponding to ±7/2 ↔ ±5/2 transition of the nuclear spin. The superconducting phase is divided into two regions by the nonsuperconducting phase, which can be understood by the appearance of a charge disproportionate state. 3) Because the increase of the crystal field q at Co sites, or the ν Q3 -increase induces the upper shift of the e g '-orbital band relatively to the a 1g one, one might expect that six hole pockets of the e g '-orbital band might be expected to appear with increasing ν Q3 in the Fermi surface near the K points in the reciprocal space. 4) If the hole pockets really appear, the ferromagnetic fluctuations with the wave vector of small q is expected to become strong and a triplet pairing state may become possible. 5) However, at least in the smaller-ν Q3 superconducting phase of the phase diagram, we have shown in previous papers that the Cooper pairs are in the singlet state, observing the suppression of the 59 Co-NMR Knight shifts by the superconductivity for both magnetic field directions parallel and perpendicular to the CoO 2 -plane. 6-8) It is consistent with results of photoemission experiments, which have observed only hole-like Fermi surface around Γ point from the a 1g -orbital band, and never ob...