  In this paper, we develop a new gravitational lensing inversion technique.
While traditional approaches assume that the lensing field varies little across
a galaxy image, we note that this variation in the field can give rise to a
``Flexion'' or bending of a galaxy image, which may then be used to detect a
lensing signal with increased signal to noise. Since the significance of the
Flexion signal increases on small scales, this is ideally suited to
galaxy-galaxy lensing. We develop an inversion technique based on the
``Shapelets'' formalism of Refregier (2003). We then demonstrate the proof of
this concept by measuring a Flexion signal in the Deep Lens Survey. Assuming an
intrinsically isothermal distribution, we find from the Flexion signal alone a
velocity width of v_c=221\pm 12 km/s for lens galaxies of r < 21.5, subject to
uncertainties in the intrinsic Flexion distribution.
