Frequency properties of infrared nonlinear s polarized surface waves, which transmit through the interface between a dielectric and a nonlinear antiferromagnet were studied. The nonlinear dispersion equation was derived. It is found that there is a critical frequency in the nonlinear s polarized surface waves. Below this frequency, the nonlinear s polarized waves on the interface are backward surface waves. Using the dispersion equation and boundary conditions, the frequency region of nonlinear s polarized waves was discussed in detail. The results show that not only the power but also the ratio of dielectric constants of two materials can influence the frequency region significantly.