A hearing instrument comprising: a BTE, Behind The Ear, part configured to be worn behind the ear of a user, the BTE part comprising: a first side, a second side substantially parallel to the first side, and a third side connecting the first side and the second side, wherein the third side is substantially perpendicular to the user's skin when the BTE part is worn behind the ear, an antenna, and a transceiver designed for transmission and reception at frequencies from 1 to 6 GHz and connected to the antenna via a non-radiating bifilar transmission line; characterized in that: the antenna comprises a radiating bifilar transmission line of the BTE part having an open connection at one end (28, 30) and comprising two conducting legs (34, 36) parallel to each other at mutual distance (W 2) of at least 2.0 mm and connected at the end opposite to the open end by an impedance matching base portion of the BTE part configured to match a lower impedance of the antenna to a higher impedance of the non-radiating transmission line of the BTE part, the non-radiating transmission line of the BTE part is connected via the impedance matching base portion to the antenna, with each one of the two strands of the non-radiating transmission line being connected to a different one of the legs of the radiating transmission line, and each leg extends in one of the opposed peripheral regions along the length of the third side of the BTE part in such a manner that the open end faces a battery of the BTE part while the base portion faces away from the battery. a BTE, Behind The Ear, part configured to be worn behind the ear of a user, the BTE part comprising: a first side, a second side substantially parallel to the first side, and a third side connecting the first side and the second side, wherein the third side is substantially perpendicular to the user's skin when the BTE part is worn behind the ear, an antenna, and a transceiver designed for transmission and reception at frequencies from 1 to 6 GHz and connected to the antenna via a non-radiating bifilar transmission line; a first side, a second side substantially parallel to the first side, and a third side connecting the first side and the second side, wherein the third side is substantially perpendicular to the user's skin when the BTE part is worn behind the ear, an antenna, and a transceiver designed for transmission and reception at frequencies from 1 to 6 GHz and connected to the antenna via a non-radiating bifilar transmission line; characterized in that: the antenna comprises a radiating bifilar transmission line of the BTE part having an open connection at one end (28, 30) and comprising two conducting legs (34, 36) parallel to each other at mutual distance (W 2) of at least 2.0 mm and connected at the end opposite to the open end by an impedance matching base portion of the BTE part configured to match a lower impedance of the antenna to a higher impedance of the non-radiating transmission line of the BTE part, the non-radiating transmission line of the BTE part is connected via the impedance matching base portion to the antenna, with each one of the two strands of the non-radiating transmission line being connected to a different one of the legs of the radiating transmission line, and each leg extends in one of the opposed peripheral regions along the length of the third side of the BTE part in such a manner that the open end faces a battery of the BTE part while the base portion faces away from the battery. the antenna comprises a radiating bifilar transmission line of the BTE part having an open connection at one end (28, 30) and comprising two conducting legs (34, 36) parallel to each other at mutual distance (W 2) of at least 2.0 mm and connected at the end opposite to the open end by an impedance matching base portion of the BTE part configured to match a lower impedance of the antenna to a higher impedance of the non-radiating transmission line of the BTE part, the non-radiating transmission line of the BTE part is connected via the impedance matching base portion to the antenna, with each one of the two strands of the non-radiating transmission line being connected to a different one of the legs of the radiating transmission line, and each leg extends in one of the opposed peripheral regions along the length of the third side of the BTE part in such a manner that the open end faces a battery of the BTE part while the base portion faces away from the battery.