An instability that leads to the filamentation of large-amplitude Alfv¿n waves and gives rise to purely growing density and magnetic field fluctuations is studied. The dispersion relation of the instability is derived, from which the threshold conditions and the growth rates of the instability are analyzed quantitatively for applications to the solar wind plasma. We have examined their dependence on the filamentation spectrum, the plasma &bgr;, and the pump frequency and intensity for both right-hand and left-hand circularly polarized Alfv¿n waves. The excitation of filamentation instability for certain cases of interest is discussed and compared with that of the parametric decay and modulation instability. The relevance of the proposed instability with some observations is discussed. ¿ American Geophysical Union 1988