Catalysis of the reaction: (1->4)-beta-D-glucuronan = an oligosaccharide with 4-deoxy-beta-D-gluc-4-enuronosyl end + (1->4)-beta-D-glucuronan. This reaction is the eliminative cleavage of (1->4)-beta-D-glucuronans to give oligosaccharides with 4-deoxy-beta-D-gluc-4-enuronosyl groups at their non-reducing ends. Complete degradation of glucuronans results in the formation of tetrasaccharides.