The invention relates to a radio-frequent (RF) coil system (17, 17') for use in a magnetic resonance imaging (MRI) system. The RF coil system comprises at least one main coil (35) for transmitting an RF magnetic field (B1) into and/or receiving an RF magnetic field (B1') from an examination volume (3) of the MRI system. The main coil has a coil axis (36), which is or is to be oriented parallel to a main magnetic field (Bo) in the examination volume (3), and at least one electrical conductor (37, 39) which extends mainly parallel to the coil axis. According to the invention, the RF coil system comprises an auxiliary coil (45, 47) which is assigned to said conductor of the main coil. The auxiliary coil has two electrical conductors (49, 51) which extend mainly parallel to the coil axis and on opposite sides of said conductor of the main coil. A distance between the two conductors of the auxiliary coil and the conductor of the main coil is small relative to a main dimension (L) of the main coil. In transmission mode, RF signals are supplied to the main coil and to the auxiliary coil with such a mutual phase difference, that a combined RF magnetic field (Bc) of 15 the main coil and the auxiliary coil has a direction of rotation (RB) opposite to a direction of precession (Rp) of the spin axes of the spinning nuclei in a body to be examined. In receiving mode, a first RF signal received by the main coil and a second RF signal received by the auxiliary coil are combined and added at such a mutual phase difference, that the second RF signal suppresses the first RF signal. In this manner, the disadvantageous high local 20 sensitivity of the RF coil system for the local region (38, 40) adjoining said conductor of the main coil is strongly reduced.