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Let X be a locally compact Hausdorff space and C 0 (X) the Banach space of continuous functions on X vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on C 0 (X). They arise from prime ideals of C 0 (X), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of c 0 can be constructed explicitly through an ultrafilter on N complementary to a cozero set ideal. Thisdoi:10.1007/s00605-003-0045-2 fatcat:ihu63qm2nvgqrafdjlqfclwkqe