A method of minimizing the consequences of an off-specification emergency landing for the occupants of a rotary wing aircraft extending from a front end towards a rear end along an anteroposterior longitudinal plane of symmetry in elevation separating a first side of said aircraft from a second side thereof, the emergency landing producing positive acceleration in a direction going from said rear end towards said front end and/or downwards, said rotary wing including at least one rotor driven in rotation by a main gearbox about an axis of rotation (AX), said rotor being provided with a plurality of blades, each blade being in an advancing position when it is on said first side relative to said longitudinal plane, moving from the rear end towards the front end, and each blade being in a retreating position when it is on said second side relative to said longitudinal plane, moving from the front end towards the rear end, said main gearbox being fastened to a structure of said aircraft by a plurality of fastener elements comprising at least one first fastener element disposed on said first side relative to said longitudinal plane and at least one second fastener element disposed on said second side relative to said longitudinal plane, in which method said first and second fastener elements are dimensioned differently so as to ensure that one of said fastener elements breaks after the other fastener element, thereby causing the main gearbox to tilt towards said second side during an off-specification emergency landing taking place under conditions lying outside the prescribed emergency landing conditions as defined by certification regulations.