Cleaning system for an external surface of a building, comprising: - a cleaning module comprising: at least one delivery nozzle configured to deliver cleaning fluid on an external surface (S) of a building (B), and a cleaning fluid tank fluidly coupled with the at least one delivery nozzle for supplying the at least one delivery nozzle with cleaning fluid; - a vertical track configured to be attached to the external surface (S) of the building (B) so as to extend in a substantially vertical direction; characterized in that the cleaning system further comprises: - a plurality of horizontal tracks configured to be attached to the external surface (S) of the building (B) so as to extend in a substantially horizontal direction and to be vertically spaced from one another, the cleaning module being movable along each horizontal track of said plurality of horizontal tracks ; - a displacement module fluidly coupled with a source of cleaning fluid ; wherein in a first operative condition of the cleaning system , the cleaning module is movable along a first horizontal track of the plurality of horizontal tracks and the displacement module is engaged with the vertical track ; and wherein in a second operative condition of the cleaning system the cleaning module is engaged with the displacement module and disengaged from the first horizontal track , the source of cleaning fluid is fluidly coupled with the cleaning fluid tank for filling the cleaning fluid tank with cleaning fluid, the displacement module is engaged with the vertical track and movable along the vertical track for displacing the cleaning module toward a second horizontal track of said plurality of horizontal tracks . - a cleaning module comprising: at least one delivery nozzle configured to deliver cleaning fluid on an external surface (S) of a building (B), and a cleaning fluid tank fluidly coupled with the at least one delivery nozzle for supplying the at least one delivery nozzle with cleaning fluid; - a vertical track configured to be attached to the external surface (S) of the building (B) so as to extend in a substantially vertical direction; - a plurality of horizontal tracks configured to be attached to the external surface (S) of the building (B) so as to extend in a substantially horizontal direction and to be vertically spaced from one another, the cleaning module being movable along each horizontal track of said plurality of horizontal tracks ; - a displacement module fluidly coupled with a source of cleaning fluid ; wherein in a first operative condition of the cleaning system , the cleaning module is movable along a first horizontal track of the plurality of horizontal tracks and the displacement module is engaged with the vertical track ; and wherein in a second operative condition of the cleaning system the cleaning module is engaged with the displacement module and disengaged from the first horizontal track , the source of cleaning fluid is fluidly coupled with the cleaning fluid tank for filling the cleaning fluid tank with cleaning fluid, the displacement module is engaged with the vertical track and movable along the vertical track for displacing the cleaning module toward a second horizontal track of said plurality of horizontal tracks . <EOS>