A method for determining a minimum-thrust descent and rejoining profile in respect of a target point by an aircraft comprises a first step of computing an energy differential of the aircraft in the air ΔEa between a first initial state of the aircraft at an initial geodesic point Qi and a second final state of the aircraft at the final arrival target point Qf. The method comprises a second step of adjusting an adjustable modelled profile of altitude hm(t) and of air speed Vam(t) of the aircraft with the aid of parameters so the adjusted modelled profile of altitude h(t) and of air speed Va(t) of the aircraft ensures the consumption of the variation of energy of the aircraft in the air ΔEa in a fixed required timespan Δtrequired and a fixed required altitude variation tf−ti in the required time timespan, the aircraft operating permanently in an engine regime with constant and minimum thrust. The method comprises a third step of determining a lateral geodesic trajectory of the aircraft on the basis of the adjusted altitude profile h(t), of the adjusted air speed profile Va(t) and of the knowledge of the speeds of the winds in the aircraft's scheduled geographical traversal zone.