It has been a long-standing problem in $N$-electron systems as to how to solve the Dyson equation with the quasiparticle wave functions defined as $\ensuremath{\langle}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{0}^{N}\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\ensuremath{\psi}}_{s}(\mathbit{r})\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{\ensuremath{\nu}}^{N+1}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rangle}$ and $\ensuremath{\langle}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{\ensuremath{\mu}}^{N\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\ensuremath{\psi}}_{s}(\mathbit{r})\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{0}^{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rangle}$, which are not mutually orthogonal and have a norm less than 1. We show that quasiparticle wave functions without multiple excitations can exactly be normalized to unity owing to the Ward identity and the vertex function in $(\mathbit{q},{\ensuremath{\omega}}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\omega})\ensuremath{\rightarrow}0$, although they are not necessarily mutually orthogonal. Since they satisfy an eigenvalue equation with the hermitized self-energy due to Baym-Kadanoff's conservation laws, the present theory can be regarded as an extension of the Kohn-Sham density functional theory, with correlated, interacting, one-electron orbitals.