  Based on an exact functional form derived for the three-point vertex function
$\Gamma$, we propose a self-consistent calculation scheme for the electron
self-energy with $\Gamma$ always satisfying the Ward identity. This scheme is
basically equivalent to the one proposed in 2001, but it is improved in the
aspects of computational costs and its applicability range; it can treat a
low-density electron system with a dielectric catastrophe. If it is applied to
semiconductors and insulators, we find that the obtained quasiparticle
dispersion is virtually the same as that in the one-shot $GW$ approximation (or
$G_0W_0$A), indicating that the $G_0W_0$A actually takes proper account of both
vertex and high-order self-energy corrections in a mutually cancelling manner.
