Disclosed is a method, for erasing data from a magnetic tape storage medium (92) housed in a cartridge (86) containing a memory in which are stored the last written track position (yy) of the last written, most recent information and the last track position (xx) of past information written in the past and remaining unerased, comprising: the step of reading out of the memory (91) the last written track position of the most recent information and the last track position of the past information; the step (S124) of determining whether the data should be erased up to the last written track position of the most recent information or up to the last track position of the past information; and the step (S126, S128) of erasing the data up to the determined position, thereby shortening the data erase time of the magnetic tape while completely solving a security problem by making provisions to completely erase the data of the most recently written information or the data of the past information written in the past and remaining unerased.