Abstract: From the nuclear Schrdinger equation of a diatomic molecule with the vibration-rotational interaction term involved in it, under the Morse potential approximation, it derives the wavefunction relevant not only with vibrational quantum number, but also with rotational one. The Franck-Condon factors of the two band systems A³Π-X³Π of BN and A¹Π-X¹∑⁺ of BH are calculated by use of the derived wavefunction. In the calculation, the rotational quantum number ranges from J=0 to J=180. The results obtained can be used in the cases under low-or high-temperature condition and also under the condition of strong shock wave.