  New distances, larger than previous ones, have been obtained for M 31 and M
81 based on the geometrical zero-point of the Cepheid Period-luminosity
relation provided by the HIPPARCOS satellite. By combining them with
independent determinations we define reasonable ranges for the distances of
these important calibrating galaxies. On this basis, we determine the Hubble
constant from the method of sosies (look-alike) galaxies, galaxies having the
same characteristics than the calibrators. The method is quite secure because
it is purely differential and it does not depend on any assumption (apart from
the natural one that two sosies galaxies have similar absolute luminosities).
Nevertheless, the Malmquist bias has to be taken into account. The observations
behave exactly as predicted from the analytical formulation of the bias. Thus,
rejecting galaxies which are affected by the Malmquist bias we derive the
Hubble constant:
  H_o = 60 +- 10 (external) km.s^{-1}.Mpc^{-1}
  If we strictly use the calibration obtained with HIPPARCOS and if the bias
found in the Period-Luminosity Relation is considered, the Hubble constant is
smaller than this ($\approx 55 km.s^{-1}.Mpc^{-1}$). This gives arguments in
favour of the long-distance scale. We briefly discuss possible improvements
aiming at still reducing the uncertainty.
