We search for a light Higgs boson (A^{0}) decaying into a τ^{+}τ^{-} or μ^{+}μ^{-} pair in the radiative decays of ϒ(1S). The production of ϒ(1S) mesons is tagged by ϒ(2S)→π^{+}π^{-}ϒ(1S) transitions, using 158×10^{6} ϒ(2S) events accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. No significant A^{0} signals in the mass range from the τ^{+}τ^{-} or μ^{+}μ^{-} threshold to 9.2 GeV/c^{2} are observed. We set the upper limits at 90% credibility level (C.L.) on the product branching fractions for ϒ(1S)→γA^{0} and A^{0}→τ^{+}τ^{-} varying from 3.8×10^{-6} to 1.5×10^{-4}. Our results represent an approximately twofold improvement on the current world best upper limits for the ϒ(1S)→γA^{0}(→τ^{+}τ^{-}) production. For A^{0}→μ^{+}μ^{-}, the upper limits on the product branching fractions for ϒ(1S)→γA^{0} and A^{0}→μ^{+}μ^{-} are at the same level as the world average limits, and vary from 3.1×10^{-7} to 1.6×10^{-5}. The upper limits at 90% credibility level on the Yukawa coupling f_{ϒ(1S)} and mixing angle sinθ_{A^{0}} are also given.