We study the effect of a large‐amplitude left‐hand polarized wave on ion acoustic instabilities. We show that the presence of a finite amplitude left‐hand polarized wave produces electrostatic instabilities above a threshold amplitude. These instabilities occur when the phase velocities of the counter‐streaming ion acoustic waves become equal, due to the action of the nonlinear wave. They do not exist in the absence of large‐amplitude waves. We examine their growth rates and threshold amplitude behavior as a function of the beam speed, temperature, and large‐amplitude wave frequency.