Study of a two-photon near resonant four wave difference mixing (FWDM) in Na in a CH4/air flame has been performed to understand the FWDM process reported by Singh and Yueh (1992). The FWDM signal was measured with reduced flame length and with the focal point at the center and also at one end of the flame to pinpoint the region in which the signal is generated. A partial contribution in the third peak was from the nonresonant background. A FWDM signal is generated slightly away from the focal point and nonresonant background, at the focal point in the present experimental conditions. An absorption spectrum of the Na D-lines at different dye laser energy was recorded to study the depletion of Na ground state at higher dye laser intensity. Comparative study of the FWDM signal with a narrow and broad bandwidth dye laser shows that a lower Na concentration detection limit could be achieved with a narrow linewidth probe laser tuned to about 9/cm lower frequency from the center of the D1 line. The two minima in the FWDM spectrum corresponding to Na D lines have been explained, qualitatively, with the saturation effect in the Na D-lines transition. 27 refs.