  Context. The wind mass transfer from a giant to its white dwarf companion in
symbiotic binaries is not well understood. For example, the efficiency of wind
mass transfer of the canonical Bondi-Hoyle accretion mechanism is too low to
power the typical luminosities of the accretors. However, recent observations
and modelling indicate a considerably more efficient mass transfer in symbiotic
binaries.
  Aims. We determine the velocity profile of the wind from the giant at the
near-orbital-plane region of eclipsing S-type symbiotic binaries EG And and SY
Mus, and derive the corresponding spherical equivalent of the mass-loss rate.
With this approach, we indicate the high mass transfer ratio.
  Methods. We achieved this aim by modelling the observed column densities
taking into account ionization of the wind of the giant, whose velocity profile
is derived using the inversion of Abel's integral operator for the hydrogen
column density function.
  Results. Our analysis revealed the spherical equivalent of the mass-loss rate
from the giant to be a few times 10^{-6}M_{Sun}/yr, which is a factor of >=10
higher than rates determined by methods that do not depend on the line of
sight. This discrepancy rules out the usual assumption that the wind is
spherically symmetric. As our values were derived from near-orbital-plane
column densities, these values can be a result of focusing the wind from the
giant towards the orbital plane.
  Conclusions. Our findings suggests that the wind from giants in S-type
symbiotic stars is not spherically symmetric, since it is enhanced at the
orbital plane and, thus, is accreted more effectively onto the hot component.
