We report a new method in the precision measurement of the refractive index of air using a highly unbalanced Michelson interferometer with a femtosecond optical frequency comb as the light source. Standard dry air is filled into a 30 m multipass cell, serving as the long arm of the interferometer, while a short arm acts as the reference path. Both time and frequency domain interferograms are recorded to measure the refractive index of air. The deviation of our experimental results with Edlen's formula is 1.4x10(-9) at 800 nm. Our experiment has a standard error of 5.2x10(-9) at fixed parameters (pressure and temperature). This is achieved by putting the multipass cell into a temperature-stabilized box, and also by locking the interferometer path length with a He-Ne laser. We achieved a temperature stabilization of 0.8 mK for 25 h. This corresponds to 0.4 mu m multipass cell length change. The locking of the He-Ne interferometer enables us to achieve 7 nm path-length change outside the multipass cell. Combined with accurate measurement of temperature and pressure, we were able to achieve an accuracy of 7.7x10(-9). (c) 2006 American Institute of Physics