An anisotropic plasma exhibits a transverse instability due to the mutual attraction of the microscopic current elements. A detailed study is made of this instability in an electron‐ion plasma without any external magnetic field. The system is characterized by a temperature tensor and described by a quasi‐Maxwellian distribution function. The dielectric tensor for such a system is calculated and then the dispersion relation is considered. It is found that there are two unstable modes: (i) a purely transverse mode and (ii) a coupled or transverse‐longitudinal mode. The latter separates into two branches: (a) the first is an essentially unstable quasitransverse mode, (b) the second is the quasi‐longitudinal ion acoustic mode driven into instability through its interaction with the quasitransverse mode. Growth rate,kand angular dependence, domain of instability, and polarization are analyzed in detail.