An investigation has been made of the hydromagnetic stability of an infinitely extended, uniformly rotating configuration of dilute plasma subjected to the influence of a strong homogeneous magnetic field. These assumptions lead to a plasma pressure of tensorial nature. The effect of self-gravitation of the medium has also been incorporated in view of its astrophysical significance. It is shown that the system is, in general, unstable. Criteria of instability in terms of pressures, parallel and perpendicular to the magnetic field, are derived for the following special cases: (a) k⊥=0, (b) k|| = 0, (c) k||→0, ω→0. k|| and k⊥ denote the propagation vectors parallel and perpendicular to the magnetic-field vector. An analogue of Jeans's condition for the fragmentation of interstellar clouds with anisotropic pressure is obtained, and it is found that the fragmentation along the magnetic-field lines is possible only if p|| < p⊥ + H2/4π.