A dual harmonization method for a head-worn display system for making the display of piloting information of an aircraft conform with the outside real world includes a step of acquisition of N measurements {circumflex over (K)}l of head postures by a series of different sightings Vi, each of which aligns a sighting pattern, situated at a different fixed position Pi on the display D0 with a sighting vector that is a function of the position Pi, then a step of computation of the matrix of relative orientation M01 between the display D0 in a tilted position of engagement in the field of view and the tracking first element D1 as the right matrix {circumflex over (D)} that is the solution of the dual harmonization system of equations Ĝ·{circumflex over (K)}i·{circumflex over (D)}·{right arrow over (x)}i={right arrow over (y)}0 for i varying from 1 to N, the vector {right arrow over (y0)} denoting the vector in the inertial reference frame of the platform corresponding to the target point targeted in the outside real world and being unknown; and the left matrix Ĝ being the matrix M23 of relative orientation between the fixed second element D2 and the attitude inertial device D3, which is potentially incorrect but assumed constant as a function of time, and which, when it is unknown, requires at least four measurements {circumflex over (K)}l. A head-up display system is configured to implement the dual harmonization method.