A method of fitting a lift to a building comprising several floors and furnished with a staircase, in which building there are between floors first stairs (4) reaching halfway to the floor level, and second stairs (5) reaching from the halfway level to next floor, and the staircase is bordered at least by one external wall (1) of the building. In the method the staircase is extended in removing the external wall that borders the staircase, and an outwards extending enlargement (12) is added, and to the building, the width of which is essentially the same as the width of the opening of the removed external wall, the second stairs are removed and moved as continuation to the first stairs, in order to form an essentially continuos ascent, possibly comprising only a small landing between the floors.