This method is an improvement to a method used to enlarge the display of a first portion of a map, without hiding a first peripheral portion of this map. This improvement involves detecting an event which appears in said first peripheral portion (SPP4′). The improvement further involves defining a second portion to be enlarged (SPA5), centered on the position (BS2) of this event, defining a second peripheral zone (SPP5) associated with this second portion to be enlarged, displaying (SPA5′) the second portion to be enlarged (SPA5) by applying respective enlargement ratios greater than 100% to at least some elements of that portion, so as to make the event more legible, and displaying (SPP5′) the second peripheral portion (SPP5) by applying at least to some elements of this portion respective enlargement ratios lower than 100% so as to save surface area to avoid hiding a portion of the map.