A Solution to the $\mu$ Problem in Gauge-mediated Supersymmetry-breaking Models

We point out that a sector required to set the cosmological constant to zero in gauge-mediated supersymmetry-breaking models naturally produces a supersymmetry-invariant mass ($\mu$ term) for Higgs doublets of the order of the electroweak scale. Since this new sector preserves the supersymmetry, it does not generate supersymmetry-breaking masses for the Higgs doublets and thus the $\mu$ problem is solved.