  In the frame of an effective MSSM model without gaugino-mass unification at a
grand unification (GUT) scale, we set a lower bound on the neutralino mass
based on the new WMAP data on $\Omega_{CDM}$. Our lower bound, $m_{\chi} \gsim
6$ GeV, leaves much room for relic neutralinos significantly lighter than those
commonly considered ($m_{\chi} \gsim 50$ GeV). We prove that these light
neutralinos may produce measurable effects in WIMP direct detection experiments
of low energy threshold and large exposure.
