  The effect of the quenched bond-randomness on the ordering of the $S=1/2$
antiferromagnetic Heisenberg model on the kagome lattice is investigated by
means of an exact-diagonalization method. When the randomness exceeds a
critical value, the ground state of the model exhibits a transition within the
non-magnetic state into the randomness-relevant gapless spin-liquid state.
Implications to the S=1/2 kagome-lattice antiferromagnet herbertsmithite is
discussed.
