<p>Starting from the fourth-order nonlinear Schrödinger equation (NLSE) the modulational instability of interfacial gravity waves on deep water in the presence of a current jump has been examined. From this equation, expressions for the growth rate of instability, perturbation wavenumber and frequency separation of the fastest growing sideband are established. It is observed that instability region increases with the increase of wave steepness but decreases with the increase of wind velocity. The key result of this work is to find the effect of flow velocity of the upper fluid on the Benjamin-Feir instability. The present fourth-order analysis shows significant deviations on the stability properties from the third-order analysis and gives better results, consistent with the exact numerical results.</p>