A navigation aid method to determine an improved trajectory between points of departure and arrival as a function of a trajectory cost, comprises: determining a grid of nodes, loading meteorological data at the nodes, determining for each node, an average instantaneous cost from a first instantaneous cost as a function of a ground speed taking into account meteorological data loaded at the node concerned, and from a second instantaneous cost as a function of a ground speed that does not take into account the loaded meteorological data, determining a length of a trajectory passing through the node and arriving at the point of arrival, determining a cost grid assigning, at each of the nodes of the grid, a local cost determined from the average instantaneous cost and the length, determining an improved trajectory from the cost grid, and graphically representing the improved trajectory and/or the cost grid to a crew.