A composition for a thermoplastic composite material having a thermoplastic matrix made of a semi-crystalline polyamide having a specific composition that includes at least two amide units, A, 55-95 mol %, and B, 5-45 mol %. A corresponds to x.T, wherein x is a C9-C18 linear aliphatic diamine and B corresponds to x′.T, wherein x′ can be B1): a specific branched x-dependent aliphatic diamine, B2): MXD or B3): a linear x-dependent aliphatic diamine, said polyamide having a glass transition temperature Tg of at least 90° C. and a melting point no higher than 280° C. Also, a method for manufacturing said composite material, the semi-crystalline polyamide polymer, the use of the composition and of the polymer for parts made of composite material, as well as the material and the resulting composite part.