A molecule that binds specifically to a human tissue plasminogen activator (TPA) or a TPA mutant is provided. The molecule having sub-nanomolar affinity to inhibit fibrin-dependent plasminogen activation with an IC50 < 5 nM, to inhibit degradation of human fibrin clots without affecting TPA amidolytic activity or non-fibrin-dependent activation, and the amino acid sequence of the TPA mutant is at least 65% identical to SEQ ID NO: 1 or SEQ ID NO: 2. Further provided is a method for treating systemic bleeding and brain hemorrhage after TPA treatment in a patient in need of such treatment. The method comprises administering to said patient an effective amount of the molecule, wherein the molecule selectively inhibits fibrin-augmented plasminogen activation in the patient.