  By using pseudopotential method with local spin density functional
approximation, the electronic band structures of Na$_{x}$CoO$_{2}$ are
calculated for $x=0.25$, 0.5, 0.75, and $x=1$ in the presence of the structure
relaxations. As increasing Na content, the hybridization between cobalt and
oxygen orbitals is decreased, and a phase transition is predicted from a
wide-band ferromagnetic to a narrow band paramagnetic metals. The itinerant
ferromagnetism is strongly suppressed by the local distortions of the oxygens
around the cobalts. Moreover, straining the CoO$_{2}$ layers corresponding to
the hydrated superconductor Na$_{0.35}$CoO$_{2}\cdot $1.3H$%_{2}$O strongly
enhances both the hybridization and ferromagnetism.
