The ion streaming instability in a dc plasma sheath with multiple ion species is studied as an eigenvalue problem. By numerically solving the eigenvalue equations of sheath plasma variables, we find a weak ion streaming instability induced in the sheath with a growth rate of a few per cent of the proton plasma frequency. The instability may provide a mechanism to enhance the collisional friction between different species of ions and result in different ions leaving the plasmas nearly at the same velocity. The effect of the species ratio on the growth rate of the instability is also discussed.