We present an empirical s-process abundance distribution derived with explicit knowledge of the r-process component in the low-metallicity globular cluster M22. We have obtained high-resolution, high signal-to-noise spectra for six red giants in M22 using the Magellan Inamori Kyocera Echelle spectrograph on the Magellan-Clay Telescope at Las Campanas Observatory. In each star we derive abundances for 44 species of 40 elements, including 24 elements heavier than zinc (Z = 30) produced by neutron-capture reactions. Previous studies determined that three of these stars (the "r + s group") have an enhancement of s-process material relative to the other three stars (the "r-only group"). We confirm that the r + s group is moderately enriched in Pb relative to the r-only group. Both groups of stars were born with the same amount of r-process material, but s-process material was also present in the gas from which the r + s group formed. The s-process abundances are inconsistent with predictions for asymptotic giant branch (AGB) stars with M <= 3M(circle dot) and suggest an origin in more massive AGB stars capable of activating the Ne-22(alpha, n)Mg-25 reaction. We calculate the s-process "residual" by subtracting the r-process pattern in the r-only group from the abundances in the r + s group. In contrast to previous r- and s-process decompositions, this approach makes no assumptions about the r- and s-process distributions in the solar system and provides a unique opportunity to explore s-process yields in a metal-poor environment.