A generalization of the HAL QCD method for lattice construction of inter-nucleon (NN) potentials is presented. It enables us to construct the NN potentials in the presence of contamination of excited states in the Nambu-Bethe-Salpeter (NBS) wave functions. For this purpose, we derive a "time-dependent" Schrödinger-like equation which describes the time-evolution of normalized four-point nucleon correlators. It makes it possible to construct the NN potentials in a smaller t region without

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... ng the ground state saturation in the four-point nucleon correlators. The time-dependent Schrödinger-like equation is applied to the NN central potential in 1 S 0 channel. The potentials obtained by using different two-nucleon source operators agree within the statistical errors.