The invention relates to a turbomachine rotary-fan blade having a predetermined breaking zone, which extends from the upstream edge along a given length and from the blade-tip edge over a given height. According to the invention, the body is made of a composite material comprising a fibre reinforcement obtained by three-dimensional weaving of warp and weft strands, and a resin matrix in which the fibre reinforcement is embedded, and has, in or in the vicinity of the zone, a discontinuity of at least some of the strands, configured such that the zone partially detaches when there is tangential friction in the thickness direction against the blade-tip edge, the height being less than 3% of the aerodynamic stream height of the blade.