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We systematically construct gauge-mediated supersymmetry(SUSY)-breaking models with direct transmission of SUSY-breaking effects to the standard-model sector. We obtain a natural model with the gravitino mass smaller than 1 keV as required from the standard cosmology. If all Yukawa coupling constants are of order one,the SUSY-breaking scale transmitted into the standard-model sector is given by $m_{SUSY} \simeq 0.1 \alpha_i/(4\pi) \Lambda\Lambda$ is the original dynamical SUSY-breaking scale. Imposing GeV, we get GeV, which yields the gravitino mass keV.

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