Patented is a closure tape for an absorbent article, such as a disposable diaper, for fastening the article to the body. The closure tape is attached to the outside surface of the diaper through one of its end portions and comprises a backing with a first and second side. The first side features a continuous or discontinuous adhesive layer, a fastening means and a stretchable elastic sheet attached to the adhesive layer. The backing is non-elastic and/or is non-extensible and the support sheet comprises the backing. The continuous or discontinuous adhesive layer exhibits one or more incisions in the elastic sheet, with one of the incisions extending in the machine direction over the full width of the backing. The end portion is separated from its closest incision to prevent the incisions from opening when attaching the end portion to the diaper’s outside surface and bending the remaining part of the closure tape to contact the inside surface of the diaper.