This invention comprises a method of treating a subject having relapsed or refractory cancer such as leukemia with liposomal annamycin including the steps of (a) evaluating the subject to determine if the subject has relapsed or refractory cancer; (b) administering a high-dose amount of liposomal-annamycin for at least 3 days in a 7 day period. First line cancer therapy with particular reference to leukemia is both contemplated and useful.