We are concerned with the least energy solution (i.e., ground state) for the following stationary nonlinear Schrödinger equation: \documentclass[12pt]{minimal}\begin{document}$-\Delta u(x)+ \lambda V(x) u(x)=K(x)f(u), \ x\break\in {\mathbb {R}^{N}}, \ N\ge 3,$\end{document}−Δu(x)+λV(x)u(x)=K(x)f(u),x∈RN,N≥3, where λ > 0, V(x) changes sign and may vanish at infinity, f(s) is superlinear or asymptotically linear at infinity. If V(x) > 0, it is shown by T. Weth [Calculus Var. Partial Differ. Equ. 27, 421 (2006)] that the energy of any sign-changing solution of the equation is larger than two times the least energy. But if V(x) changes sign, we find that the equation does have a sign-changing ground state for λ > 0 large. Moreover, our results show that it is impossible to get a solution of the equation by seeking a minimizer of the energy functional of the equation over the so called Nehari manifold when V(x) changes sign.