Abstract: We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N₂ and O₂ molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N₂ and O₂ molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of $\sigma$  and $\pi$  orbitals, the bonding orbital ($\sigma _{2pz})^2$ of N₂ determines the maximum of harmonic emission when the molecular axis of N₂ is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O₂ molecule the antibonding orbitals ($\pi _{2py}^\ast )^1$ and ($\pi _{2pz}^\ast )^1$ contribute to the maximum of harmonic yield when O₂ is aligned at 45$^{\circ}$ and bonding orbitals ($\pi _{2py} )^2$ and ($\pi _{2pz} )^2$ slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45$^{\circ}$.

Key words: harmonic emission, valence orbital, space rotation operator, molecular orientation