We report on the spatio-temporal dynamics of the interface in shear-banding
flow of a wormlike micellar system (cetyltrimethylammonium bromide and sodium
nitrate in water) during a start-up experiment. Using the scattering properties
of the induced structures, we demonstrate the existence of an instability of
the interface between bands along the vorticity direction. Different regimes of
spatio-temporal dynamics of the interface are indentified along the stress
plateau. We build a model based on the flow symetry which qualitatively
describes the observed patterns