A method for making a composite part comprising a thermoplastic polymer matrix and comprising a web and at least two flanged edges (552, 553), at least one of the flanged edges being oriented with respect to the web at an angle (591, 592) of less than 90°, the method using a tooling comprising: - a die comprising an imprint comprising an opening, an entry width, a bottom and side walls - a punch comprising a central part and at least two lateral movable parts (121, 122, 321, 322, 323, 324) in sliding connection with the central part comprising an end between the lateral parts and forming a wedge between said lateral parts, pressure means between the lateral movable parts and the central part; - means for moving the punch relative to the die in a striking direction; - configured so that a width of the punch is less than the entry width of the opening of the imprint and in which the lateral parts are stopped in translation in the striking direction against the bottom of the die, the displacement of the central part in this same direction relative to the lateral parts causes a relative displacement of the lateral parts in directions (291, 292) of lateral expansion of the punch, a width of the expanding punch being equal to or greater than the entry width of the opening of the die; - the wedge-shaped central part (123, 423) comprising two parts (123 1, 123 2) and inbetween these two parts,, means (127, 427 1, 427 2) for adjusting a width of the central part in the directions of lateral expansion; the method comprising the steps of: - pairing the punch and the die by adjusting the means (127, 427 1, 427 2) for adjusting the width of the central part of the punch according to the thicknesses of the core and the flanged edges of the part; - obtaining a composite blank whose width (616, 617) is greater than the width of the opening of the die; - heating the composite blank at a temperature equal to or higher than a melting temperature of the thermoplastic polymer matrix; - positioning the composite blank above the die of the tooling and stamping the composite blank between the punch and the imprint along a stroke in the striking direction until the lateral parts reach a distance from the bottom of the imprint equal to a thickness of the web; - continuing the stroke of the punch to move the lateral parts up to distances from the side walls of the imprint equal to the thicknesses of the flanged edges and compact the part; - cool down the part under pressure between the punch and the imprint to a temperature lower than the melting temperature of the polymer matrix to consolidate the part; - move the punch away from the die and unmold the part. - a die comprising an imprint comprising an opening, an entry width, a bottom and side walls - a punch comprising a central part and at least two lateral movable parts (121, 122, 321, 322, 323, 324) in sliding connection with the central part comprising an end between the lateral parts and forming a wedge between said lateral parts, pressure means between the lateral movable parts and the central part; - means for moving the punch relative to the die in a striking direction; - configured so that a width of the punch is less than the entry width of the opening of the imprint and in which the lateral parts are stopped in translation in the striking direction against the bottom of the die, the displacement of the central part in this same direction relative to the lateral parts causes a relative displacement of the lateral parts in directions (291, 292) of lateral expansion of the punch, a width of the expanding punch being equal to or greater than the entry width of the opening of the die; - the wedge-shaped central part (123, 423) comprising two parts (123 1, 123 2) and inbetween these two parts,, means (127, 427 1, 427 2) for adjusting a width of the central part in the directions of lateral expansion; - pairing the punch and the die by adjusting the means (127, 427 1, 427 2) for adjusting the width of the central part of the punch according to the thicknesses of the core and the flanged edges of the part; - obtaining a composite blank whose width (616, 617) is greater than the width of the opening of the die; - heating the composite blank at a temperature equal to or higher than a melting temperature of the thermoplastic polymer matrix; - positioning the composite blank above the die of the tooling and stamping the composite blank between the punch and the imprint along a stroke in the striking direction until the lateral parts reach a distance from the bottom of the imprint equal to a thickness of the web; - continuing the stroke of the punch to move the lateral parts up to distances from the side walls of the imprint equal to the thicknesses of the flanged edges and compact the part; - cool down the part under pressure between the punch and the imprint to a temperature lower than the melting temperature of the polymer matrix to consolidate the part; - move the punch away from the die and unmold the part.