A method (50) for reprogramming a computer (10) by modification of the content of a non-volatile rewritable memory (104) of the computer via reprogramming software stored in the non-volatile rewritable memory (104). The reprogramming software includes a task sequencer and a plurality of software components, divided in advance into at least two sets, namely: a first set including each software component to be executed simultaneously with an operation of modifying the content of the non-volatile rewritable memory (104), and a second set including some or all of the other software components of the reprogramming software. During the reprogramming of the computer, the software components of the second set are executed from the non-volatile rewritable memory (104), and the task sequencer and the software components of the first set to be executed are copied in advance into a volatile memory (106) of the computer, and are executed from the volatile memory.