  Magnetic excitations in the spin-$\frac{1}{2}$ distorted kagome lattice
antiferromagnet Cs$_2$Cu$_3$SnF$_{12}$, which has an ordered ground state owing
to the strong Dzyaloshinskii-Moriya interaction, were studied using inelastic
neutron scattering. Although the spin-wave dispersion can be qualitatively
understood in terms of linear spin-wave theory (LSWT), the excitation energies
are renormalized by a factor of approximately 0.6 from those calculated by
LSWT, almost irrespective of the momentum transfer. This inadequacy of LSWT,
which is attributed to quantum fluctuations, provides evidence of negative
quantum renormalization in the spin-$\frac{1}{2}$ kagome lattice
antiferromagnet.
