An antenna arrangement comprises a radiating antenna element (101), feed point (304, 703, 804) for connecting the radiating antenna element to a radio apparatus, and a ground plane (303, 705, 808). There is between the feed point and ground plane a certain shortest distance which is substantially greater than 1.5 mm. The antenna arrangement has two different operating frequency bands. Preferably the construction comprises an electrically conductive connecting component (105, 603, 801) for connecting the radiating antenna element to the feed point, a functional part (110, 809) in the radio apparatus for transmitting and receiving electromagnetic radiation through an antenna, and a transmission line (306, 604, 605) for providing an electrical connection between the connecting component and the functional part in the radio apparatus. The transmission line comprises in succession a first portion (307, 604) and a second portion (308, 605) such that the longer the distance between a given reference point in the first portion and the interface between the first portion and second portion, the greater the shortest distance between the reference point and the ground plane, and the shortest distance between a given reference point in the second portion and the ground plane is independent of the distance between the reference point and said interface.