A hair extension (1 ), of the kind particularly used for the thickening of hair, has a linear fixing member (2) from which hairs (3) perpendicularly branch, arranged in a flat configuration, wherein: the linear fixing member (2) is formed by two flexible tapes (4, 5) adhered to each other so as to obtain a fixing strip, with hairs embedded between the two flexible tapes (4, 5) due to a fixing adhesive layer (6) arranged therebetween the tapes being flexible and made of thermoplastic material the tapes (4, 5) being provided with a plurality of passing through holes all over the surface thereof the linear fixing member (2) has at least one uncovered adhesive face provided with a pressure-activated and non-permanent further adhesive layer (8) and the tapes (4, 5) has been pressed against each other, so that the hairs (3) and the adhesive material of the fixing adhesive layer (6) are at least partially penetrated into said passing through holes, said exposed adhesive face embodies the support surface for a plurality of peelable films (9), each separated from others by a further non-permanent adhesive layer (8), the surfaces thereof being apt to be uncovered have, with respect to said layer (8), an adhesiveness greater than the rear surface of each film (9), so that said surfaces apt to be uncovered be adhesive surfaces, allows both a permanent application, through thermowelding of the fixing member, and non permanent, achieved thank to the outer adhesive layer, which can be identically repeated as many times as the number of available peelable films, then once more when the flexible tapes are directly connected to the receiving hair.Linvention concerne une extension (1) de cheveux du type particulièrement utilisé pour épaissir les cheveux, qui comporte un élément (2) de fixation linéaire doù les cheveux (3) se ramifient perpendiculairement, disposé en une configuration plane. Selon linvention, lélément (2) de fixation linéaire est constitué de deux bandes (4, 5) souples
