  The rare $K^\pm\to\pi^\pm\pi^0 e^+e^-$ decay, currently under analysis by the
NA48/2 Collaboration, is considered. We have performed two theoretical
approaches to calculate the differential decay width -- in the kaon rest frame,
where we use Cabibbo-Maksimovicz variables, and in the center-of-mass system of
the lepton pair. The latter essentially simplifies the computations. A
comparison between the two approaches has been performed. We have also found
the dependencies of the differential decay rate as a function of the virtual
photon and dipion system masses
