We have employed second-order coherence function theory to study the nonlinear effects of third-and fifth-order on polarization beats in a four-level system (TPBFS and FPBFS). It is found that the different temporal behavior of the beat signal in TPBFS and FPBFS depends on the stochastic properties of the lasers and transverse relaxation rate of the transition. We have considered the cases that pump beams have either narrow band or broadband linewidth and found that for both cases a Doppler-free precision can be achieved in the measurement of the energy-level difference between two excited states which are dipolar forbidden from the ground state. We also discussed the spatiall modulation behavior of the beat signal.