The excitation of slow waves by the fast wave antenna could lead to the undesirable heating of plasma periphery and must be suppressed. The effects of slow wave excitation are analyzed using a one dimensional analytical model. The effect of conversion of fast wave to slow wave at the plasma edge is discussed. The efficiency of the slow wave generation with the different components of the alternating current and the surface charge which is induced on the antenna current-carrying elements is studied. Qualitatively, the minimum slow wave excitation could be achieved if: the electrostatic fields induced by the antenna are shielded effectively; the currents in the antenna elements and those ones induced in the shield by the antenna magnetic and electrostatic fields are directed mainly perpendicular to the steady magnetic field. In practice, both the requirements above mentioned could not met rigorously. Thus, all the existing antennas excite slow waves. Prom this point of view, properties of unshielded and shielded strap antennas are discussed. A new antenna which provides the minimum slow wave excitation is proposed. It consists of the strap current-carrying element and a number of grounded shield elements of the similar design. The antenna impedance properties are analyzed in the framework of the continuos one-dimensional model. The analysis showed that the antenna impedance could be lower than that one for simple strap antenna. Like a TEM-mode transmission line it has resonances which could be used for decreasing the reactive part of the impedance which makes easier the matching of the antenna with feeding electric circuits. The newly proposed antenna could be used both in large scale and small plasma devices. The experimental testing of it in a mirror device in comparison with a standard strap antenna is of primary interest.