The invention relates to a method of manufacturing a semiconductor device (10) with a substrate (11) and a semiconductor body (12) which is provided with at least one bipolar transistor having an emitter region (1), a base region (2) and a collector region (3), wherein in the semiconductor body (12) a first semiconductor region (13) is formed that forms one (3) of the collector and emitter regions (1,3) and on the surface of the semiconductor body (12) a stack of layers is formed comprising a first insulating layer (4), a polycrystalline semiconductor layer (5) and a second insulating layer (6) in which stack an opening (7) is formed, after which by non-selective epitaxial growth a further semiconductor layer (22) is deposited of which a monocrystalline horizontal part on the bottom of the opening (7) forms the base region (2) and of which a polycrystalline vertical part (2A) on a side face of the opening (7) is connected to the polycrystalline semiconductor layer (5), after which spacers (S) are formed parallel to the side face of the opening (7) and a second semiconductor region (31) is formed between said spacers (S) forming the other one (1) of the emitter and collector regions (1,3). According to the invention the above method is characterized in that before the further semiconductor layer (22) is deposited, the second insulating layer (6) is provided with an end portion (6A) that viewed in projection overhangs an end portion (5A) of the underlying semiconductor layer (5). In this way bipolar transistor devices can be obtained with good high frequency properties in a cost effective manner.