The present invention relates to a repositionable bandage including an adhesive hydrocolloid mass, wherein said bandage includes, on at least one portion of the surface of the adhesive mass intended for being in contract with the wound when the bandage is being used, a web of microfibers or nanofibers, at least 90% and preferably at least 95% of which being made up of one (or more) material(s) selected among natural or synthetic polymers, and being suitable for solubilizing or gelling in under ten seconds, and preferably still in less than one second when in contact with the exudate from the wound. The bandage according to the invention is intended for treating wounds such as blisters, exuding wounds, burns and dermal-epidermal lesions, whether superficial, deep, chronic or acute.