A self-adhesive band or complex has a textile support structure with a coating for securing to the skin of a wearer. The textile support structure includes an extensible, aerated, finely knitted or woven support structure having, at least on its inner face, a thin coating having immediate and high adhesive properties. The coating has a degree of softness to conform to microreliefs of the wearer's skin, and an elastic modulus at least as low as that of the substrate against which it is in contact to match the microreliefs thereof.