The use of L-carnitine or one of its pharmaceutically acceptable salts is described for the preparation of a medicine useful for reducing the number of deaths caused by acute myocardial infarction and for improving the short-and-long-term prognosis in the patients treated with it, in which L-carnitine is administered parenterally within the first few hours of onset of the symptoms of acute myocardial infarction at an initial dose of 9 grams a day for 5 days, after which the treatment is continued at a dose of 4 grams a day by the enteral route