We have searched for neutralinos produced via the reactions e+e− → χχ′ and e+e−→ χ′χ′, where the next-to lightest neutralino, χ′, decays into the lightest neutralino, χ, and either a photon or a fermion pair. Based on 1.8 × 106 hadronic Z decays collected with the L3 detector at LEP, no signal has been observed. We present upper limits of a few times 10−5 on the branching ratios Z → χχ′ and Z → χ′χ′. In the framework of the Minimial Supersymmetric Standard Model, we exclude a lightest χ with mχ less than 18 GeV, if either tan β > 2 or the gluino mass m≈g > 100 GeV.