Magnetic recording media comprising a non-magnetic base and, applied thereto, a firmly adhering magnetic coating based on a finely divided magnetic pigment dispersed in a binder which contains at least 50 percent by weight of a special polyurethane elastomer, namely a thermoplastic polyurethane which is soluble in tetrahydrofuran, is free from isocyanate groups and has been manufactured from (A) 1 mole of a hydroxyl-containing polyester having a molecular weight of from 700 to 2,500, (B) from 0.3 to 3 moles of a linear aliphatic diol of 2 to 10 carbon atoms, (C) from 0.05 to 0.4 mole of a triol of 3 to 10 carbon atoms, and (D) from 1.35 to 4.7 moles of a diisocyanate of 6 to 30 carbon atoms, the amount of NCO groups being approximately equivalent to the amount of OH groups of the sum of components (A) to (C).