  Energies and transition probabilities of K$\beta$ hypersatellite lines are
computed using the Dirac-Fock model for several values of $Z$ throughout the
periodic table. The influence of the Breit interaction on the energy shifts
from the corresponding diagram lines and on the K$\beta\_{1}^{\rm
h}$/K$\beta\_{3}^{\rm h}$ intensity ratio is evaluated. The widths of the
double-K hole levels are calculated for Al and Sc. The results are compared to
experiment and to other theoretical calculations.
