Catalysis of the reaction: a pectate = a pectate + a pectate oligosaccharide with 4-(4-deoxy-alpha-D-galact-4-enuronosyl)-D-galacturonate end. This reaction is the eliminative cleavage of pectate to give oligosaccharides with 4-deoxy-alpha-D-gluc-4-enuronosyl groups at their non-reducing ends.