1. A method for facilitating a search for a target in a multispectral image, said multispectral image comprising several spectral intensity values relating respectively to several distinct spectral bands (B1-B16), for each point of an image matrix ( 1 ) and for a same scene (S) which is imaged on said image matrix for all the spectral bands, said method comprising the following sequence of steps, executed for an observation window ( 2 ) which is smaller than the image matrix ( 1 ): /1/ selecting the window in the image matrix; /2/ selecting a direction of projection in a multidimensional space of the spectral intensities so as to optimize within the window ( 2 ) a contrast of an intermediate image of the scene which is formed by using for each point in said window a projection of the spectral intensity values associated with said point onto the selected direction of projection, and /3/ displaying a detection image corresponding to the entire image matrix ( 1 ), said detection image being produced, for the points located inside the window ( 2 ), from the intermediate image for the selected direction of projection, and supplemented for the points located outside of the window so that said detection image represents the entire scene which is imaged, wherein the optimization in step /2/ is applied to a set of points of the image matrix ( 1 ), said set being limited to inside the window ( 2 ) and comprising at least one point in said window.