A method and an arrangement uses an extra member intended to be connected to the ordinary grounding plane system of an antenna through a portion a the coaxial input terminal sleeve being present outside the case of an apparatus. The extra member is tuned in such a way that it preferably operates as an electrical quarter-wave radiator in a range at the upper limit of a designed operating frequency range, while the remaining effective grounding plane system of the antenna is preferably tuned to a frequency in a range at the lower limit of the intended operating frequency range, where, for instance, a portable radio telephone should operate, to in this way obtain an increased bandwidth and a reduced influence of immediate surrounding environment of the antenna of the portable equipment.