A new method is presented for computation of diatomic rotational line strengths, or Hönl-London factors. The traditional approach includes separately calculating line positions and Hönl-London factors and assigning parity labels. The present approach shows that one merely computes the line strength for all possible term differences and discards those differences for which the strength vanishes. Numerical diagonalization of the upper and lower Hamiltonians is used, which directly obtains the line positions, Hönl-London factors, total parities, and e/f parities for both heteronuclear and homonuclear diatomic molecules. The FORTRAN computer program discussed is also applicable for calculating n-photon diatomic spectra.