  We investigate the chiral phase transition in the strong coupling lattice QCD
at finite temperature and density with finite coupling effects. We adopt one
species of staggered fermion, and develop an analytic formulation based on
strong coupling and cluster expansions. We derive the effective potential as a
function of two order parameters, the chiral condensate sigma and the quark
number density $\rho_q$, in a self-consistent treatment of the next-to-leading
order (NLO) effective action terms. NLO contributions lead to modifications of
quark mass, chemical potential and the quark wave function renormalization
factor. While the ratio mu_c(T=0)/Tc(mu=0) is too small in the strong coupling
limit, it is found to increase as beta=2Nc/g^2 increases. The critical point is
found to move in the lower T direction as beta increases. Since the vector
interaction induced by $\rho_q$ is shown to grow as beta, the present trend is
consistent with the results in Nambu-Jona-Lasinio models. The interplay between
two order parameters leads to the existence of partially chiral restored
matter, where effective chemical potential is automatically adjusted to the
quark excitation energy.
