A secure element includes a boot program comprises instructions for the execution a startup step to determine if a non-volatile memory stores an active operating system, and, in the affirmative, to launch execution of the operating system, an authentication step of a updater device, as a function of first authentication data determined by a secure element and second authentication data received from the updater device, and, in response to the authentication step, a storage step of a new operating system received from the update, device in the non-volatile memory and an activation step of the new operating system, when said instructions are executed by a microprocessor.