The present invention relates to an openwork prosthetic knit (1) made from a single piece based on at least a first yarn made of biocompatible polymer material that defines a first face (2) and a second face that are opposite one another and from a second biocompatible yarn that generates barbs (5) that protrude outwards from at least said first face, characterized in that said first face comprises at least one longitudinal strip (4) in the direction of the manufacture of said knit, over which it is provided with said barbs (5), and at least one longitudinal strip (3) in the direction of the manufacture of said knit, over which it is free of such barbs. It also relates to a process for manufacturing such a knit (1) and to a prosthesis comprising such a knit (1).