The invention relates to a composition including: 45 to 95 wt % of a semi-aromatic copolyamide containing at least two separate units having the following general formulation: A/X.T, where A is selected from among a unit obtained from an amino acid, a unit obtained from a lactam, and a twit having the formula (diamine Ca).(diacid Cb), and XT denotes a unit obtained from the polycondensation of a diamine in Cx and from terephthalic acid, with x being the number of carbon atoms of the diamine in Cx, said copolyamide having a polymoleoularity index, noted Ip, of less than or equal to 3.5, measured by gel permeation chromatography, and an amino chain end content of between 0.020 mcg/g and 0.058 mcg/g; and 5 to 55 wt % of at least one cross-linked polyolefin. The invention also relates to a method for preparing said composition and to the uses thereof.