In lipid monolayers consisting of two phases, the competition between line tension and electrostatic repulsion can give rise to a stripe phase. The stability of this phase with respect to small harmonic distortions is analyzed. It is shown that the stripe phase is just marginally stable when the stripes are of equilibrium width. As soon as the stripes exceed this width, coupled long wavelength distortions are energetically favored. Intermediate results concerning the stability of a single edge and a single stripe are also presented.