  We present the first "clipped" cosmic shear measurement using data from the
Kilo-Degree Survey (KiDS-450). "Clipping" transformations suppress the signal
from the highest density, non-linear regions of cosmological fields. We
demonstrate that these transformations improve constraints on
$S_8=\sigma_8(\Omega_{\rm{m}}/0.3)^{0.5}$ when used in combination with
conventional two-point statistics. For the KiDS-450 data, we find that the
combined measurements improve the constraints on $S_8$ by 17%, compared to
shear correlation functions alone. We determine the expectation value of the
clipped shear correlation function using a suite of numerical simulations, and
develop methodology to mitigate the impact of masking and shot noise. Future
improvements in numerical simulations and mass reconstruction methodology will
permit the precise calibration of clipped cosmic shear statistics such that
clipping can become a standard tool in weak lensing analyses.
