  Weak gravitational lensing flexions are a kind of weak lensing distortion
which are defined as the spin 1 and spin 3 combinations of the third order
derivatives of gravitational lensing potential. Since the shear has spin 2
combination of the second order derivative, the flexion signal gives a partly
independent information from shear signal and is more sensitive to the local
mass distribution than shear signal. Thus its measurement is expected to play
important roles in observational cosmology. However, since the weakness of the
flexion signal as well as the complicatedness of its intrinsic noise made its
accurate observation very difficult. We propose a new method of measuring the
flexion signal using ERA method which is a method to measure weak lensing shear
without any approximation. We find two particular combinations of the flexions
which provide the quantities with only lensing information and free of
intrinsic noise when taken average. It is confirmed by simple numerical
simulation that the statistical average of these combinations do not in fact
depend on the strength of the intrinsic distortion.
