  The recently discovered sharp peak in the excitation function of the K+/pi+
ratio around 30 A GeV in relativistic heavy-ion collisions is discussed in the
framework of the Statistical Model. In this model, the freeze-out of an ideal
hadron gas changes from a situation where baryons dominate to one with mainly
mesons. This transition occurs at a temperature T = 140 MeV and baryon chemical
potential mu(B) = 410 MeV corresponding to an energy of sqrt(s) = 8.2 GeV. The
calculated maximum in the K+/pi+ ratio is, however, much less pronounced than
the one observed by the NA49 Collaboration. The smooth increase of the K-/pi-
ratio with incident energy and the shape of the excitation functions of the
Lambda/pi+, Xi-/pi+ and Omega/pi ratios all exhibiting maxima at different
incident energies, is consistent with the presently available experimental
data. The measured K+/pi+ ratio exceeds the calculated one just at the incident
energy when the freeze-out condition is changing.
  We speculate that at this point freeze-out might occur in a modified way. We
discuss a scenario of an early freeze-out which indeed increases K+/pi+ ratio
while most other particle ratios remain essentially unchanged. Such an early
freeze-out is supported by results from HBT studies.
