Many diseases are dominated by persistent growth of capillary blood vessels. Tumor growth is also angiogenesis-dependent. Safe and effective angiogenesis inhibitors are needed to determine whether control of angiogenesis would be therapeutic. Heparin and certain steroids, administered together, can inhibit angiogenesis in a synergistic manner. This "pair" effect suggested that specific hydrophilic cycloamyloses may be suitable heparin substitutes. beta-Cyclodextrin tetradecasulfate administered with a steroid inhibits angiogenesis at 100 to 1000 times the effectiveness of heparin in the chick embryo bioassay. This cyclic oligosaccharide also augments the anti-angiogenic effect of angiostatic steroids against corneal neovascularization in rabbits when beta-cyclodextrin tetradecasulfate and a steroid are inserted into the cornea or applied topically as eyedrops.