Catalysis of the hydrolysis of (2->6)-beta-D-fructofuranan, to remove successive disaccharide residues as levanbiose, i.e. 6-(beta-D-fructofuranosyl)-D-fructose, from the end of the chain.
2,6-beta-D-fructan 6-beta-D-fructofuranosylfructohydrolase activity