Magnetic field generation in a relativistic plasma in the presence of Langmuir or electromagnetic waves is studied theoretically. The generation is shown to occur in the form of the three simplest instabilities: anisotropic, magnetic-modulational and magnetic-transformational, or their combinations. Characteristic wave numbers and growth rates of the instabilities mentioned are found as function of the degree of plasma relativism. The growth rates are shown to attain their maxima at relativistic temperatures.