  Measurements of the magnetization under high hydrostatic pressure (up to 10.2
kbar) in YBa_2Cu_4O_8 were carried out. From the scaling analysis of the
magnetization data the pressure induced shifts of the transition temperature
T_c, the volume V and the anisotropy \gamma have been obtained. It was shown
that the pressure induced relative shift of T_c mirrors essentially that of the
anisotropy. This observation uncovers a novel generic property of anisotropic
type II superconductors, that inexistent in the isotropic case.
