A system for an aircraft comprising a controller configured to obtain a first piece of information regarding whether the aircraft has achieved lift-off; to obtain a second piece of information regarding whether the aircraft is in a flight phase in an initial part of lift-off; to determine, on the basis of at least the first piece of information whether the gear is retractable, and, if the gear is retractable in an initial part of the lift-off, to trigger a landing-gear-retraction alarm taking an audio form and/or a visual form, and, if the gear is retractable after the initial part of the lift-off to optionally trigger a second landing-gear-retraction alarm taking an audio form and/or a visual form. A method implemented by the system is provided. Advantageously, an omission of the retraction of the landing gear of an aircraft is notified to its flight crew.