Conventional chemical approaches to protein-protein coupling present challenges due to the intrinsic competition between the desired interactions of reagents with groups of the protein as well as reactions with water. Biorthogonal Cu(i)-catalyzed azide-alkyne cycloaddition (CuAAC)-processes provide a basis to direct reactivity without functional group interference. However, the requirement for Cu(i) in CuAAC leads to complications that result from the metal ion's interactions with the protein. In principle, a similar but metal-free alternative approach to coupling could employ the reaction of an alkyne that is strained in combination with an azide (strain-promoted azide-alkyne cycloaddition, SPAAC). The method is exemplified by the combination of a cyclooctyne derivative of hemoglobin with an azide-modified hemoglobin. The bis-hemoglobin tetramer that is produced has properties consistent with those sought for use as a hemoglobin-based oxygen carrier (HBOC).