The experimental data on antilambda and direct antiproton
production, measured near midrapidity in central heavy-ion collisions at AGS energies, show that the ratio antilambda/antiproton = 3.6 is well above theoretical estimates. We argue that the anomally large value of the ratio can be explained by non-uniform distribution of net strangeness and net baryon charge within the volume of the
fireball. To demonstrate this idea a simple two-source statistical model is employed. Though the sources are assumed to be in chemical and thermal equilibrium, their temperatures and chemical potentials are allowed to be different. Only 4pi-data are used for the statistical analysis of heavy-ion central collisions. It is shown
also that the antilambda/antiproton ratio, obtained for the
central source, drops from 3.5 to unity with the rise of incident energy from AGS to SPS, in full accord with the experimental results at midrapidity.