Cleaves the beta-1,4-linkages between beta-D-galactose and alpha-L-3,6-anhydro-galactose residues in agarose. Cleaves agarose in a random manner with retention of the anomeric-bond configuration, producing beta-anomers that give rise progressively to alpha-anomers when mutarotation takes place. Also tolerant to hybrid substrates containing C6-sulfate groups at the -4, +1, and +3 positions. Hydrolysis of (1->4)-beta-D-galactosidic linkages in agarose, giving the tetramer as the predominant product. kcat is 100 sec(-1). Homodimer. When cells are grown with the low sulfated agar. Belongs to the glycosyl hydrolase 16 family.