Transistor and method of manufacturing a bipolar transistor of the double-polysilicon, heterojunction-base type, in which a semiconducting layer with SiGe heterojunction is formed by non-selective epitaxy on an active region of a substrate and an insulating region surrounding the active region. At least one stop layer is formed on the semiconducting layer above a part of the active region. A layer of polysilicon and an upper insulating layer are formed on the semiconducting layer and on a part of the stop layer, leaving an emitter window free. An emitter region is formed by epitaxy in the emitter window, resting partially on the upper insulating layer and in contact with the semiconducting layer.