The wig or hairpiece is fixed on the head of the wearer by pulling the existing natural hair strands through the fabric support of the wig. Special holes in the fabric have rectangular or square clamping features for the natural hair. The natural hair strands(c) are held in clamping features(d) which have preferably elastic wire supports. These supports are arranged symmetrically over the circumference of the web strip of the wig support fabric (b). The wire inserts are fitted into the pocket (a) distributed on the web strip and pushed into it. The fastening arrangement is a conventional press stud with the stud and reinforced head and sockets d of press studs are distributed over the circumference of wig fabric web strip.