A power series mathematical solution is advanced for the problem of instability of an inviscid liquid sheet of parabolic velocity profile emanated from a nozzle into an inviscid gas. A comparison of the instability of a sheet of parabolic velocity profile with one of a uniform velocity profile is performed in order to deduce the effects of velocity profile relaxation on instability. The results show that for both antisymmetrical and symmetrical disturbances departure from uniformity of the velocity profile causes the instability to be reduced. The physical interpretation and practical implications of the present findings are discussed. ©1998 American Institute of Physics.