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In particular, we show that if |V(x)|\\les \\la x \\ra ^{-3-} and there is only s-wave resonance at zero of H, then \\big\\| w^{-1} \\big( e^{itH}P_{ac} f - {\\f 1 t } F f \\big) \\big\\| _{\\infty} \\leq \\frac {C} {|t| (\\log|t|)^2 } \\|wf\\|_1 |t|>2, with w(x)=\\log^2(2+|x|). Here Ff=c \\psi\\la f,\\psi \\ra, where \\psi is an s-wave resonance function. 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