A carbon molecular sieve (CMS) membrane having improved separation characteristics for separating olefins from their corresponding paraffins is comprised of carbon with at most trace amounts of sulfur and a transition metal, wherein the transition metal is one or more of a group 4-10 and 12 transition metal. The CMS membrane may be made by pyrolyzing a precursor polymer devoid of sulfur in which the precursor polymer has had a transition metal incorporated into it. The pyrolyzing for the precursor having the transition metal incorporated into it is performed in a nonoxidizing atmosphere and at a heating rate and temperature such that the metal has a valence greater than zero (i.e., not metal bonded) to a valence desirably closer to its maximum valence.