A bandage has first and second adhesive areas on corresponding end portions of the bandage for adhering the bandage to the skin of a user, and a wound dressing pad between the two adhesive areas. Portions of first and second cover strips are disposed to protect corresponding adhesive areas on the bandage. A bandage wrapper envelopes the bandage including the cover strips, and the cover strips themselves are bonded by an adhesive to a confronting surface of the wrapper. Thus, when a user pulls the ends of the wrapper apart to open the wrapper and remove the bandage, each cover strip is peeled away from the bandage by a part of the wrapper to which the cover strip is bonded. The dressing pad on the bandage is then exposed to be applied on a wound without having to come in contact with the users hands.
