A thermoplastic polyurethane can be obtained by a process involving a reaction of a thermoplastic polyester (PE-1) with a diamine (D1), to obtain a composition (Z1) containing an amide (PA-1), and a reaction of the obtained composition (Z1) with an isocyanate composition (I1), containing at least one polyisocyanate, and a polyol composition (P1). The diamine (D1) has a molecular weight in the range from 50 g/mol to 700 g/mol. A process can produce such a thermoplastic polyurethane, and shaped articles can be made containing the thermoplastic polyurethane.