Abstract: A method, computer program and system are provided for calculating in an automatic manner a trajectory for rejoining a reference vertical profile of an aircraft. A reference vertical profile comprises a set of vertical constraints, and a method comprises a step of selecting an altitude constraint to be complied with, a step of calculating a vertical-profile prediction making it possible to comply with the constraint, a step of validating the vertical-profile prediction, if the vertical-profile prediction is validated, a step of applying the vertical-profile prediction, otherwise a step of determining the existence of a following altitude constraint to be complied with; if a following altitude constraint exists: a step of selecting a following altitude constraint to be complied with; a return to the step of detecting non-compliance with an altitude constraint; otherwise, a step of applying an exit procedure.