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The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential $i{\partial }_{t}u+1/2\Delta u-1/2\left|x\right|²u=-{\left|u\right|}^{4/(d-2)}u,x\in {ℝ}^d$, is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.