A new method is proposed for extracting limits on spin-dependent WIMP-nucleon interaction cross sections from direct detection dark matter experiments. The new method has the advantage that the limits on individual WIMP-proton and WIMP-neutron cross sections for a given WIMP mass can be combined in a simple way to give a model-independent limit on the properties of WIMPs scattering from both protons and neutrons in the target nucleus. Extension of the technique to the case of a target material consisting of several different species of nuclei is discussed. PACS: 95.35.+d; 12.60.Jv; 14.80.Ly Keywords: dark matter; WIMP; neutralino; supersymmetry e-mail: firstname.lastname@example.org 1 Introduction Weakly Interacting Massive Particles (WIMPs) are believed to be the most plausible candidate for dark matter (DM) in the Universe. WIMPs are predicted to exist in many extensions of the Standard Model of particle physics. Most of the well-motivated WIMP candidates are Majorana (i.e., = ) f..