A theory on polarized infrared external reflection spectroscopy (ERS) of a uniaxial monolayer at the air/water interface was described. Some aspects of this theory, such as the optimal incidence angle, the orientation-frequency correlation; and the surface selection rule were addressed. The most important theme is to obtain the anisotropic complex refractive indexes of the monolayer. A monolayer of F(CF2)(4)(CH2)(22)COOH at the, interface of air and the aqueous Cd2+ subphase was chosen as an example. The Langmuir-Blodgett (LB) technique was applied to deposit the monolayer onto solid substrates. The anisotropic complex refractive indexes were obtained from infrared measurements of the monolayer on the solid substrates. By use of these-optical constants, the polarized ERS spectrum of the monolayer on the aqueous Cd2+ subphase was simulated and compared to the experimental one. The comparison sorted out artifacts associated with the LB transfer process and unambiguously predicted the molecular orientation at the air/water interface. It is concluded that at the optimal incidence angle of 80degrees, the p-polarized ERS method can achieve an accuracy of +/-1degrees in locating the average orientation angle of a transition dipole moment (TDM). This case happens when the TDM is oriented near the vanishing angle. The TDM orientation angle of the CH2 antisymmetric stretching vibration along the -(CH2)(22)- chain was determined to be 56degrees +/-1degrees on the aqueous Cd2+ subphase at 283 K and 20 mN/m. On the other hand, the best accuracy of the s-polarized ERS method can achieve is +/-2degrees. The validity of the polarized ERS theory was checked by comparing the present orientation angles with previous ones obtained from polarization-modulated ERS measurements. Finally, a high precision attachment for the water surface measurement was employed, guaranteeing the quantitative aspect of the ERS spectra.