A magnetic recording medium comprising a non-magnetic base and, applied thereto, a firmly adhering magnetic coating consisting essentially of a dispersion of a magnetic pigment in a binder which contains at least 50 percent by weight of a thermoplastic polyurethane which is soluble in tetrahydrofuran, is free from isocyanate groups, has high surface hardness and a high modulus of elasticity and which has been made by reaction of (A) 1 mole of one or more hydroxyl-containing polyesters and/or one or more hydroxyl-containing polyethers having a molecular weight of from 600 to 4,000, wherein said hydroxyl-containing polyester is formed by esterification of aliphatic dicarboxylic acids of 4 to 12 carbon atoms, carboxylic acid esters of 1 to 4 carbon atoms in the alcohol radical, carboxylic acid anhydrides or carboxylic acid chlorides with aliphatic glycols of 2 to 12 carbon atoms which may contain ether groups, or by polymerization of cyclic lactones of 3 to 6 carbon atoms and wherein said hydroxyl-containing polyether is formed by polymerization of cyclic ethers or by reaction of one or more alkylene oxides of 2 to 4 carbon atoms in the alkylene oxide radical with a starter molecule which contains two active hydrogen atoms, in the presence as a chain extender of (B) from 3.5 to 15 moles of a branched-chain aliphatic diol containing from 4 to 10 carbon atoms or a mixture of aliphatic diols containing from 2 to 10 carbon atoms, of which diol mixture at least 50 mole percent is branched-chain and contains from 4 to 10 carbon atoms and (C) from 0 to 1 mole, but not more than 15 mole percent on the basis of the aforesaid aliphatic diol(s) of an aliphatic polyol containing from 3 to 6 hydroxy groups and from 3 to 18 carbon atoms, which (D) from 4.5 to 18 moles of an aromatic diisocyanate containing from 6 to 30 carbon atoms, the amount of isocyanate groups present in the reaction being approximately equivalent to the amount of hydroxy groups in the components A to C.