bandage (n.)

"strip of soft cloth or other material used in binding wounds, stopping bleeding, etc.," 1590s, from Middle French bandage (16c.), from Old French bander "to bind," from bande "a strip" (see band (n.1)).

"to dress a wound, etc., with a bandage," 1734 (implied in bandaging), from bandage (n.). Related: Bandaged.