Catalyzes the NAD-dependent decarboxylation of UDP-glucuronic acid to UDP-xylose. Necessary for the biosynthesis of the core tetrasaccharide in glycosaminoglycan biosynthesis. H(+) + UDP-alpha-D-glucuronate = CO2 + UDP-alpha-D-xylose Nucleotide-sugar biosynthesis; UDP-alpha-D-xylose biosynthesis; UDP-alpha-D-xylose from UDP-alpha-D-glucuronate: step 1/1. Ubiquitous. Belongs to the NAD(P)-dependent epimerase/dehydratase family. UDP-glucuronic acid decarboxylase subfamily.