The spectrum of B²S⁺–R²S⁺ system of AlO has been recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.05 cm^-1. Nineteen bands of the Du = 1, 0, -1, and -2 sequences of this band system have been analyzed for the rotational structure. Out of which seven bands, viz. 3–2, 4–3, 2–3, 3–4, 4–5, 5–6 and 6–7 have been analyzed for the first time. The rotational lines of these 19 bands along with 20 earlier analyzed bands, a total of 7200 lines, have been fitted in a simultaneous least squares fit. The study has resulted in determining more precise vibrational and rotational constants of the two states. Because of the high resolution employed it became necessary to invoke H₀ and H₁ coefficients, and a fifth order term to explain the anomalous spin-doubling observed in the u" = 5, 6 and 7 levels of the X²S⁺ state.