Encoded digital information signals are magnetically recorded on a magnetic recording medium with the assistance of a magnetic head to which write current is supplied. As a function of the encoded information signals, a head change is carried out wherein the current applied to the magnetic head is changed from a first current value to a second current value and vice versa. After each head change, an amplitude of the write current is varied in stepwise amounts from the first or second current value, respectively, and wherein the number of steps depends on a chronological spacing of the head changes from one another. Distortions of resulting read signals are reduced given the method and apparatus of the invention.