The present invention provides non-anticoagulant sulfated or sulfonated polysaccharides (NASPs), which accelerate the blood clotting process. Also provided are pharmaceutical formulations comprising a NASP of the invention in conjunction with a pharmaceutically acceptable excipient and, in various embodiments, these formulations are unit dosage formulations. The invention provides a NASP formulation, which is orally bioavailable. Also provided are methods for utilizing the compounds and formulations of the invention to promote blood clotting